Question

Henry and Irene working together can wash all the windows of their house in 1h 48m. Working alone, it takes Henry 1.5 h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
Please show equation.

Answer 1

anybody?

Answer 2

Yeah, hold on..

Answer 3

It takes them 1hr 48 min=1.8 hours to do one job.
So they can do 1/1.8=5/9 jobs per hour.
So if Henry's rate alone is x jobs per hour, Irene's is (5/9-x) jobs per hour.
Thus, it takes 1/x hours for Henry to do 1 job, while it takes Irene 1/(5/9-x)=9/(5-9x) hours.
Now, it takes Henry 1.5 hours longer than Irene, so 1/x=9/(5-9x)+3/2

Solving this yields:

2(5-9x)=18x+3x(5-9x)
10-18x=18x+15x-27x^2
27x^2-51x+10=0
(9x-2)(3x-5)=0
x=2/9 or x=5/3.
We test these:

If Henry's rate is 2/9, then Irene's is 5/9-2/9=3/9
If his rate is 5/3, hers is -10/9.

Since the second solution is negative for Irene's rate, we throw it out, and that leaves us with:

Henry's rate=2/9 jobs/hour, so he can complete a job in 9/2=4.5 hours.
Irene's rate=3/9 jobs/hour, so she can complete a job in 9/3=3 hours.

(Not that the second solution is also strangely plausible. It just means that Irene dirties the windows at a rate of -10/9 per hour. Thus, Henry would do a job in 3/5 hours, while Irene at -9/10 hours. Thus, with Henry cleaning the windows, and Irene dirtying them at a slower rate, the job will still get done in 1.8 hours. But my guess is that they want the positive answer.)

Answer 4

First word in the parentheses should be Note*