# The time taken by Henry and Irene alone to wash all the windows. ### 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 65E
To determine

## To find: The time taken by Henry and Irene alone to wash all the windows.

Expert Solution

The time taken by Henry is 4.5 hours and time taken by Irene is 3 hours.

### Explanation of Solution

Given:

Henry and Irene work together and wash all the windows in 1 hr 48 min.

Henry takes 112 hr more than Irene to complete the work.

Calculation:

Let the time taken by Irene be x.

Tabulate the given information into the language of algebra.

 In words In Algebra Time taken by Irene x hr Time taken by Henry (x+1.5) hr Time taken by both 1.8 hr Work done by Irene in 1 hr 1x Work done by Henry in 1 hr 1x+1.5 Work done by both in 1 hr 11.8

Model the equation for the above information.

(FractiondonebyHenry)+(FractiondonebyIrene)=Fractiondonebyboth1x+1x+1.5=11.8

Simplify the above equation for x,

(x+1.5)+x=x(x+1.5)1.8(MultiplybyLCD2.5x)1.8(2x+1.5)=x(x+1.5)3.6x+2.7=x2+1.5xx22.1x2.7=0

Factor the above equation for x,

(x3)(x+0.9)=0x=3,x=0.9

Time cannot be negative. So Irene takes 3 hours to wash all the windows.

Time taken by Henry to wash all windows,

x+1.5=3+1.5=4.5

Henry takes 4.5 hours to wash all windows.

Thus, the time taken by Henry is 4.5 hours and time taken by Irene is 3 hours.

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