BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 65E

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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