# The time taken by Karen to paint the house alone.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.6, Problem 63E
To determine

## To find: The time taken by Karen to paint the house alone.

Expert Solution

The time taken by Karen to paint the house is 3 hour.

### Explanation of Solution

Given:

Betty takes 6 hour to paint the house and if they work together than they take two-thirds the time taken by Karen.

Calculation:

Let the time taken by Karen to paint the house be x.

Tabulate the given information into the language of algebra.

 In words In Algebra Time taken by Karen x hr Time taken by Betty 6 hr Time taken by both 2x3 Work done by Karen 1x Work done by Betty 16 Work done by Karen and Betty 32x

Model the equation for the above information.

FractiondonebyKaren+FractiondonebyBetty=Fractiondonebyboth1x+16=32x

Simplify the above equation for x,

6+x=3×3(MultiplybyLCD6x)6+x=9x=3

Thus, the time taken by Karen to paint the house is 3 hour.

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