Math Word Problems Demystified - A Self Teaching Guide

time. Also, the amount of work done by a single person, machine, or pipe is

equal to the rate times the time, that is,

RateTime¼Amount of work done

EXAMPLE:Frank can cut a lawn in 2 hours. His brother Jeff can cut the

same lawn in 3 hours. How long will it take them if they cut the lawn at the

same time?

SOLUTION:

GOAL: You are being asked to find the time in hours it will take both boys

to cut the grass if they work together.

STRATEGY: Letx¼the time it takes them if they work together. Now, in

one hour, Frank can cut^12 of the lawn and Jeff can cut^13 of the lawn.

Rate  Time ¼Amount of work done

Frank^1

2

x^1

2

x

Jeff^1

3

x^1

3

x

Frank does^12 xorx 2 amount of work and Jeff does^13 xorx 3 amount of

work. These are the fractional parts of work done by each. Then the

total amount of work done is 100% or 1. The equation is

x

2

þ

x

3

¼ 1

The LCD of 2 and 3 is 6, so clear fractions:

63

1



x

21

þ

62

1



x

31

¼ 6  1

3 xþ 2 x¼ 6

5 x¼ 6

51 x

5

¼

6

5

x¼ 1 :2 hours

182 LESSON 17 Solving Work Problems