Problems about NumbersIf one more than three times a number is divided by the number, the result is four thirds. Find the number.

3x

3 3 1x xx

3 3 1 4x x

9 3 4x x

5 3x 35

x

LCD = 3x1x

43

3

3 4x

9 4 3x x

5.6 – Applications

Problems about Work Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can sort a batch in 3 hours. If they work together, how fast can they sort one batch?

Time to sort one batch (hours)

Fraction of the job completed in one hour

Ryan

Mike

Together

12131x

2

3

x

5.6 – Applications

Problems about Work Time to sort

one batch (hours)

Fraction of the job completed in one hour

Ryan

Mike

Together

12131x

2

3

x

12 6 1

2x

3x 5 6x 65

x hrs.

LCD =13

1x

6x 3

6 1x 16x

x

2x 6115

5.6 – Applications

James and Andy mow lawns. It takes James 2 hours to mow an acre while it takes Andy 8 hours. How long will it take them to mow one acre if they work together?

Time to mow one acre (hours)

Fraction of the job completed in one hour

James

Andy

Together

2

8

x

12181x

5.6 – Applications

Time to mow one acre (hours)

Fraction of the job completed in one hour

James

Andy

Together

2

8

x

12181x

LCD:12

8 12

x

4x 5 8x 85

x

hrs.

18

1x

8x 8

8 1x 18x

x

x 8315

5.6 – Applications

A sump pump can pump water out of a basement in twelve hours. If a second pump is added, the job would only take six and two-thirds hours. How long would it take the second pump to do the job alone?

112

1x

263

1203

Time to pump one basement (hours)

Fraction of the job completed in one hour

1st pump

2nd pump

Together

x

12

203

5.6 – Applications

112

1x

263

1203

Time to pump one basement (hours)

Fraction of the job completed in one hour

1st pump

2nd pump

Together

x

12

112

1 112 x

203

1x

1203

320

5.6 – Applications

LCD:

60 112

x

5x

60 4xhrs. 15x

1 1 312 20x

60x

160x

x 0

60 32

x

60 9x

5x60 9x

5.6 – Applications

Distance, Rate and Time Problems If you drive at a constant speed of 65 miles per hour and you travel for 2 hours, how far did you drive?

d r t

65mileshour

2 hours 130 miles

d tr

d rt

5.6 – Applications

A car travels six hundred miles in the same time a motorcycle travels four hundred and fifty miles. If the car’s speed is fifteen miles per hour faster than the motorcycle’s, find the speed of both vehicles.

Rate Time Distance

Motor-cycle

Car

x

x + 15

450 mi

600 mi

t

t

rdt

x450

15600x

5.6 – Applications

Rate Time Distance

Motor-cycle

Car

x

x + 15

450 mi

600 mi

t

t

rdt

x450

15600x

x450

15

600x

LCD: x(x + 15)

15600450

xx

x(x + 15) x(x + 15)

5.6 – Applications

15600450

xx

x(x + 15) x(x + 15)

xx 60045015

xx 60015450450

x15015450

x

15015450

x45

45x mphMotorcycle

6015 x mphCar

5.6 – Applications

Rate Time Distance

UpStream

DownStream

A boat can travel twenty-two miles upstream in the same amount of time it can travel forty-two miles downstream. The speed of the current is five miles per hour. What is the speed of the boat in still water? boat speed = x

x - 5

x + 5

22 mi

42 mi

t

t

rdt

522x

542x

5.6 – Applications

Rate Time Distance

UpStream

DownStream

boat speed = x

x - 5

x + 5

22 mi

42 mi

t

t

rdt

522x

542x

522x

5

42x

LCD: (x – 5)(x + 5)

542

522

xx(x – 5)(x + 5) (x – 5)(x + 5)

5.6 – Applications

542225 xx

2104211022 xx

xx 2242210110

x20

320

x1616 mph

Boat Speed

542

522

xx(x – 5)(x + 5) (x – 5)(x + 5)

x20320

5.6 – Applications

2855

Review of Long Division

783 4

4 7835 2855

2535

7

350

438362

19

3

5

203

5.7 – Division of Polynomials

43195

43195

72812 2 xxxx4

xx 48 2 x6 7

3

36 x

4

12 x

12434x

x 728 2 xx

124

x

Long Division

12728 2

xxx

5.7 – Division of Polynomials

35125 2 xxxx

xx 52 x7 35

7

357 x

0

5x 7x 35122 xx

Long Division

535122

xxx

5.7 – Division of Polynomials

15023 2 xxxx2

xx 62 2 x6 15

6

186 x

3

3x

3362x

x 152 2 x

33

x

Long Division

3152 2

xx

5.7 – Division of Polynomials