Math Word Problems Demystified - A Self Teaching Guide

Rate  Time ¼Amount of work done

First cleaner^1

8

x^1

8

x

Assistant cleaner^1

12

x^1

12

x

Since the assistant starts two hours later, the first cleaner has already

done 2^18 or^28 of the work. Hence, the equation is

2

8

þ

1

8

xþ

1

12

x¼ 1

IMPLEMENTATION: Solve the equation:

2

8

þ

1

8

xþ

1

12

x¼ 1

The LCD is 24.

243

1



2

81

þ

243

1



x

81

þ

242

1



x

121

¼ 24  1

6 þ 3 xþ 2 x¼ 24

6 þ 5 x¼ 24

6 
 6 þ 5 x¼ 24 
 6

51 x

51

¼

18

5

x¼ 3 :6 hours

Since the person has already worked two hours, the time it takes to clean
the whole building is 2þ3.6¼5.6 hours.

EVALUATION: Check the equation:

2

8

þ

1

8

xþ

1

12

x¼ 1

Usex¼3.6.

LESSON 17 Solving Work Problems 185