SOLUTION: Henry and Irene working together can wash all the windows of their house in 1 h 24 min. Working alone, it takes Henry 4 1/2 h more than Irene to do the job. How long does it take e

Question 497435: Henry and Irene working together can wash all the windows of their house in 1 h 24 min. Working alone, it takes Henry 4 1/2 h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Henry and Irene working together can wash all the windows of their house in 1 h 24 min. Working alone, it takes Henry 4 1/2 h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
**
let x=hours Irene takes to do the job alone
1/x=Irene's work rate
x+4.5=hours Henry takes to do the job alone
1/(x+4.5)=Henry's work rate
1 hr and 24 min=1.4 hr=Irene and Henry working together to do the job
1/1.4=Their work rate working together
..
sum of individual work rates=work rate when working together
1/x+1/(x+4.5)=1/1.4
LCD:(x)(x+4.5)(1.4)
(x+4.5)(1.4)+1.4x=(x)(x+4.5)
1.4x+6.3+1.4x=x^2+4.5x
x^2+1.7x-6.3=0
solve by quadratic formula as follows:
..

..
a=1, b=1.7, c=-6.3
x=[-1.7�√(1.7^2-4*1*-6.3)]2*1
x=[-1.7�√28.09]/2
x=(-1.7�5.3)/2
x=-7/2=-3.5 (reject, x>0)
or
x=3.6/2=1.8
ans:
It takes Irene 1.8 hrs or 1 hr and 45 minutes to do the job alone.
Henry takes 4.5 hrs longer or 6.3 hr or 6 hrs and 18 minutes to do the job alone.
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