Intermediate Algebra (11th edition)

Solving a Work Problem

It takes two carpet layers 4 hr to carpet a room. If each worked alone, one of them

could do the job in 1 hr less time than the other. How long would it take each carpet

layer to complete the job alone?

Step 1 Readthe problem again. There will be two answers.

Step 2 Assign a variable.Let the number of hours for the slower carpet layer

to complete the job alone. Then the faster carpet layer could do the entire job in

hours. The slower person’s rate is and the faster person’s rate is

Together, they do the job in 4 hr.

1

x- 1.

1

1 x- (^12) x,

x=

EXAMPLE 3

514 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

Recall from Section 7.5that a person’s work rate is part of the job per hour,

where tis the time in hours required to do the complete job. Thus, the part of the

job the person will do in xhours is^1 t x.

1

t

PROBLEM-SOLVING HINT

Multiply by the LCD,

x 1 x- 12.

Time Working Fractional Part

Rate Together of the Job Done

4

4 1

x- 1

(^1 142)
x- 1
1
x^142
1
x Sum is 1
whole job.
Slower
Worker
Faster
Worker

Step 3 Write an equation.

Part done by slower worker Part done by faster worker 1 whole job

1

Step 4 Solvethe equation from Step 3.

Distributive property

Distributive property

Standard form

This equation cannot be solved by factoring, so use the quadratic formula.

Quadratic formula

Simplify.

x= Use a calculator.

9 + 265

2

L8.5 or x=

9 - 265

2

L0.5

x=

9  265

2

x = a=1, b=-9, c= 4

- 1 - 92  21 - 922 - 4112142

2112

x=

- b 2 b^2 - 4 ac

2 a

x^2 - 9 x+ 4 = 0

4 x- 4 + 4 x= x^2 - x

41 x- 12 + 4 x= x 1 x- 12

x 1 x- 12 a

4

x

+

4

x- 1

b = x 1 x- 12112

=

4

x- 1

+

4

x

+ =

Complete

a table.