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.