6.7 Practice Problems

Math 98

Instructions

Each problem in this slide show is worked out step-by-step.

For each problem, try to work it out by yourself first. If you get stuck read through my solution until you get unstuck then work it from there.

Then check your work against mine. Remember, you need to use an equation with a variable to solve each problem.

Some Advice

• Always define your variable to represent one of the quantities you are being asked for.

• This section is based on rational problems, your equation should be a rational equation.

• Your equation should be meaningful. If you can’t express it in a sentence, it isn’t correct.

Number Puzzles

The first two problems are about solving for numbers.

Problem #1

Find two consecutive even integers such

that the sum of their reciprocals is .24

7

Problem #1 (step 1)

Find two consecutive even integers such

that the sum of their reciprocals is .

Define your variable.

Express all unknown quantities in terms of

that variable.

24

7

Problem #1 (step 1)

Find two consecutive even integers such

that the sum of their reciprocals is .

Define your variable.

Let x be the first even integer.

Express all unknown quantities in terms of

that variable.

x + 2 is the second even integer.

24

7

Problem #1 (step 2)

Find two consecutive even integers such

that the sum of their reciprocals is .

Write an equation using your variable and

the information in the problem as it is

written.

24

7

Problem #1 (step 2)

Find two consecutive even integers such

that the sum of their reciprocals is .

Write an equation using your variable and

the information in the problem as it is

written.

24

7

24

7

2

11

xx

Problem #1 (step 3)

Solve the equation.

24

7

2

11

xx

Problem #1 (step 3)

Solve the equation.

LCD is 24x(x + 2) 24

7

2

11

xx

Problem #1 (step 3)

Solve the equation.

LCD is 24x(x + 2) 24

7

2

11

xx

Problem #1 (Step 4)Find two consecutive even integers such

that the sum of their reciprocals is .

Answer the question asked.

Problem #1 (Step 4)Find two consecutive even integers such

that the sum of their reciprocals is .

Answer the question asked.

Because x is an integer, it must be 6.

x = 6, thus x + 2 = 8

6 and 8 are the two consecutive even integers.

Problem #2

The sum of the reciprocal of a number and the reciprocal of four less than the number is six times the reciprocal of the original number. Find the original number.

Problem #2

The sum of the reciprocal of a number and the reciprocal of four less than the number is six times the reciprocal of the original number. Find the original number.

Define your variable.

Express all unknown quantities in terms of that

variable.

Problem #2

The sum of the reciprocal of a number and the reciprocal of four less than the number is six times the reciprocal of the original number. Find the original number.

Define your variable.

Let n be the number.

Express all unknown quantities in terms of that

variable.

n – 4 is four less than the number.

Problem #2

The sum of the reciprocal of a number and the reciprocal of four less than the number is six times the reciprocal of the original number. Find the original number.

Write an equation using your variable and the information in the problem as it is written.

Problem #2

The sum of the reciprocal of a number and the reciprocal of four less than the number is six times the reciprocal of the original number. Find the original number.

Write an equation using your variable and the information in the problem as it is written.

Problem #2Solve the equation.

Problem #2Solve the equation.

LCD is

Problem #2Solve the equation.

LCD is

Problem #2

The sum of the reciprocal of a number and the reciprocal of four less than the number is six times the reciprocal of the original number. Find the original number.

Answer the question asked.

Problem #2

The sum of the reciprocal of a number and the reciprocal of four less than the number is six times the reciprocal of the original number. Find the original number.

Answer the question asked.

5 is the original number.

Note: It’s also good to double check the answer. In this case, four less than 5 is 1. The sum of the reciprocals of 5 and 1 are:

Which is what we were looking for.

Motion Problems

Remember when you are setting up the problem that you can define a variable to represent the quantity you are looking for.Also, your equation can now be about time, rate, or distance.

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Rate (mph) Time (hours) Distance (miles)

Upstream 2

Downstream 10

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Use the formula to fill in the time column.

Rate (mph) Time (hours) Distance (miles)

Upstream 2

Downstream 10

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Use the formula to fill in the time column.

Rate (mph) Time (hours) Distance (miles)

Upstream 2

Downstream 10

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Because the time column is where all the information comes together, create an equation about time.

Rate (mph) Time (hours) Distance (miles)

Upstream 2

Downstream 10

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Because the time column is where all the information comes together, create an equation about time.

Rate (mph) Time (hours) Distance (miles)

Upstream 2

Downstream 10

Problem #3 (Motion)

Solve the equation.

Problem #3 (Motion)

Solve the equation.

Cross Multiply.

Problem #3 (Motion)

Solve the equation.

Cross Multiply.

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Answer the question asked.

Problem #3 (Motion)Garth likes to kayak in the river. One day he went kayaking. He was told that the current of the river was 2 miles per hour. If it took Garth the same amount of time to travel 10 miles downstream as 2 miles upstream, determine the speed of his kayak in still water.

Answer the question asked.

Garth kayaks at a rate of

3 miles per hour in still water.

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.Identify and organize the information we have already and define a variable to represent what we’re looking for.

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.Identify and organize the information we have already and define a variable to represent what we’re looking for.

Rate Time Distance

Subaru 376

Explorer 368

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.Identify and organize the information we have already and define a variable to represent what we’re looking for.

Use the formula to fill in the time column.

Rate Time Distance

Subaru 376

Explorer 368

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.Identify and organize the information we have already and define a variable to represent what we’re looking for.

Use the formula to fill in the time column.

Rate Time Distance

Subaru 376

Explorer 368

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.

Because the time column is where all the information comes together, create an equation about time.

Rate Time Distance

Subaru 376

Explorer 368

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.

Because the time column is where all the information comes together, create an equation about time.

Rate Time Distance

Subaru 376

Explorer 368

Problem #4 (Motion)

Solve the equation.

Problem #4 (Motion)

Solve the equation.

Cross Multiply.

Problem #4 (Motion)

Solve the equation.

Cross Multiply.

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.Answer the question asked.

Problem #4 (Motion)A Subaru Outback travels 1 mile per hour faster than a Ford Explorer. In the time it takes the Explorer to travel 368 miles, the Outback travels 376 miles. Find the speed of each vehicle.Answer the question asked.

Looking back at our table, represents the rate of the Explorer.

Answer: The Subaru travels 47 mph and the Explorer travels 46 mph.

Rate

Subaru = 47

Explorer = 46

Problem #5 (Motion)

Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Problem #5 (Motion)

Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Problem #5 (Motion)

Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Rate (mph) Time (hours) Distance (miles)

Uphill 5

Downhill 8

Problem #5 (Motion)

Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Use the formula to fill in the time column.

Rate (mph) Time (hours) Distance (miles)

Uphill 5

Downhill 8

Problem #5 (Motion)

Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Identify and organize the information we have already and define a variable to represent what we’re looking for.

Use the formula to fill in the time column.

Rate (mph) Time (hours) Distance (miles)

Uphill 5

Downhill 8

Problem #5 (Motion)Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Because the time column is where all the information comes together, create an equation about time.

Rate (mph) Time (hours) Distance (miles)

Uphill 5

Downhill 8

Problem #5 (Motion)Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Because the time column is where all the information comes together, create an equation about time.

Be careful with units on this one!

Rate (mph) Time (hours) Distance (miles)

Uphill 5

Downhill 8

Problem #5 (Motion)Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Because the time column is where all the information comes together, create an equation about time.

Be careful with units on this one!

Rate (mph) Time (hours) Distance (miles)

Uphill 5

Downhill 8

Problem #6 (Motion)

Solve the equation.

Problem #6 (Motion)

Solve the equation.

LCD is 120.

Problem #6 (Motion)

Solve the equation.

LCD is 120.

Problem #5 (Motion)

Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Answer the question asked.

Problem #5 (Motion)

Jamie ran up to the top of the hill at 5 miles per hour. She then turned around and ran back down the hill at 8 miles per hour. If her total running time was 26 minutes, how far is it to the top of the hill?

Answer the question asked.

The distance to the top of the hill is 1 and 1/3 miles.

Work and Drain ProblemsThe key here is that the rate at which a person (or machine or other) does a job, is the reciprocal of the time it takes them to do it.

(Rate)(Time) = work done.

You add the efforts to get one job done (=1) if everyone is working towards the same goal.

You subtract the efforts to get one job done (=1) if people, machines, pipes, etc are working against each other.

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

rate  = 1Alone

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

rate  = 1Alone

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

rate  = 1Alone

Work = (rate)(time)

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

rate  = 1Alone

Work = (rate)(time)

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Use this information to create an equation.

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Use this information to create an equation.

They are working together, so

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Use this information to create an equation.

They are working together, so

Working Alone (hrs)

Rate (rooms/hr)

Time Together (hrs)

Work Done (rooms)

Adriel 4

Max 6

Problem #6 (Work/Drain)

Solve the equation.

Problem #6 (Work/Drain)

Solve the equation.

LCD is 24

Problem #6 (Work/Drain)

Solve the equation.

LCD is 24

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Answer the question asked.

Problem #6 (Work/Drain)Adriel can paint the living room in 4 hours, but it takes Max 6 hours. How long would it take them to paint the living room if they worked together?

Answer the question asked.

2 hours 24 minutes(Or 2.4 hours)

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

rate  = 1Alone

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

rate  = 1Alone

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

rate  = 1Alone Work = (rate)(time)

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

rate  = 1Alone Work = (rate)(time)

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Use this information to create an equation.

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Use this information to create an equation.

They are working together, so

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Use this information to create an equation.

They are working together, so

Working Alone (hrs)

Rate (fences/hr)

Time Together (hrs)

Work Done (fences)

Antonio 12

Carlotta

Problem #7 (Work/Drain)

Solve the equation.

Problem #7 (Work/Drain)

Solve the equation.

LCD is

Problem #7 (Work/Drain)

Solve the equation.

LCD is

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Answer the question asked.

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Answer the question asked.

Problem #7 (Work/Drain)Antonio can paint a fence by himself in 12 hours. With Carlotta’s help it only takes 5 hours. How long would it take Carlotta to paint the fence by herself?

Answer the question asked.

Note: On an exam provide an exact answer unless asked for the decimal approximation.

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (documents/hr)

Time Working (hrs)

Work Done (documents)

First Scanner

3 .5

Second Scanner

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (documents/hr)

Time Working (hrs)

Work Done (documents)

First Scanner

3 .5

Second Scanner

rate  = 1Alone

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (documents/hr)

Time Working (hrs)

Work Done (documents)

First Scanner

3 .5

Second Scanner

rate  = 1Alone

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (documents/hr)

Time Working (hrs)

Work Done (documents)

First Scanner

3 .5

Second Scanner

rate  = 1Alone Work = (rate)(time)

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (hrs)

Rate (documents/hr)

Time Working (hrs)

Work Done (documents)

First Scanner

3 .5

Second Scanner

rate  = 1Alone Work = (rate)(time)

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Use the information to create an equation.

Working Alone (hrs)

Rate (documents/hr)

Time Working (hrs)

Work Done (documents)

First Scanner

3 .5

Second Scanner

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Use the information to create an equation.

Working Alone (hrs)

Rate (documents/hr)

Time Working (hrs)

Work Done (documents)

First Scanner

3 .5

Second Scanner

Solve the equation.

Problem #8 (Work/Drain)

Solve the equation.

The Least Common Denominator is .

Problem #8 (Work/Drain)

Solve the equation.

The Least Common Denominator is .

Problem #8 (Work/Drain)

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Answer the question asked.

Problem #8 (Work/Drain)A large, multi-page document can be scanned by one scanner in 3 hours. After the first scanner has worked for 1 hour, a second scanner is added to the job. It takes an additional 1.5 hours to scan the rest of the document. How long would it take to scan the whole document on just the second scanner?

Answer the question asked.

9 hours

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

rate  = 1Alone

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

rate  = 1Alone

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

rate  = 1Alone

Work = (rate)(time)

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Identify the information you know already and assign a variable to the quantity for which you are being asked.

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

rate  = 1Alone

Work = (rate)(time)

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Use the information to create an equation.

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Use the information to create an equation.

The two processes are working against each other, so

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Use the information to create an equation.

The two processes are working against each other, so

Working Alone (mins)

Rate (tubs/min)

Time Together (min)

Work Done (tubs)

Fill 10

Drain

Problem #9 (Work/Drain)

Solve the equation.

Problem #9 (Work/Drain)

Solve the equation.

The LCD is 30.

Problem #9 (Work/Drain)

Solve the equation.

The LCD is 30.

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Answer the question asked.

Problem #9 (Work/Drain)A certain bathtub can be filled in 10 minutes and drained in 6 minutes. If the water is running and the drain is open, how long will it take for the tub to empty? Assume the tub starts out full.

Answer the question asked.

15 minutes