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Solving Math Word Problems
ACC Summer Institute 2005
Fidel Rodriguez
Jimmy Clark
Time and Distance Word Problems
Basic Concepts
d = distance
r = rate of speed
t = time
d = r X t
r = d / t
t = d / r
Process for Solving Math Word Problems
Follow these steps to solve math word problems:
1. State what is given
2. State what is required
3. Solve problem
4. Prove your solution
A Helpful Hint
Create a table or grid on paper or in Word. Sample columns:
Row headings d = r X (times) t
Solving a Sample Distance Problem
A 555-mile plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
Purple Math Website
• This problem comes from the website of Purple Math, a great resource for all sorts of information about mathematics. The URL for this website is:
Using the 4-Step Process to Solve the Problem
1. Given: d = 555 milest = 5 hoursr = 105 mph for first part of tripr = 115 mph for second part of journey
Equation: d = r X t
Using the 4-Step Process to Solve the Problem (Cont)
2. Requested: Time (t) traveled at each rate of speed
Set up Table / Grid
d = r X t
First Part d = 105 X t
Second Part 555 – d = 115 X 5 - t
TOTAL 555 5
SOLUTION: d = 105t
555 – d = 115(5-t)
Add Equations 555 = 105t + 115(5-t)
Simplify 555 = 105t + 575 – 115t
Add and Subtract
555 = -10t + 575
Solution Continued
d = r X t
Add and Subtract 555 = -10t + 575
Simplify 555 – 575 = -10t
Add and Subtract -20 = -10t
Minuses cancel out 10t = 20
Solve for t t = 2
The plane traveled at 105 mph for 2 hours.
t for 2nd part of trip: 5 – t = 5 -2 = 3
The plane traveled at 115 mph for 3 hours.
Prove Your Solution
First Part: d = 105 X td = 105 X 2d = 210 miles
Second Part: d = 115 X td = 115 X 3d = 345 miles
Total: d = First Part + Second Partd = 210 + 345d = 555 miles
Credits
Let the Credits Roll
We hope you enjoyed this presentation on how to solve distance word problems. This movie was produced by Fidel Rodriguez, Assistant Professor of Mathematics, Austin Community College and Jimmy D. Clark, Instructional Design Specialist, Austin Community College.
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