Answer:
Step-by-step explanation:
Henry and Irene working together can wash all the windows of their house in 1 h 40 min. Working alone, it takes Henry 2 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 us represent
The number of hours Irene takes to do the job alone =x
1/x=Irene's work rate
The number of hours Henry takes to do the job alone = x + 2.5
1/(x+2.5)=Henry's work rate
1 hr and 40 min
Converting the 40 minutes to hour
60 mins = 1 hour
40 mins = x
x = 40/60
x = 0.6666666667 hour
1 hour 40 minutes = 1.67hours
Irene and Henry working together to do the job
Their work rate working together
sum of individual work rates=work rate when working together
1/x+1/(x+2.5)=1/1.67
LCD:(x)(x+2.5)(1.67)
(x+2.5)(1.67)+(1.67)(x)=(x)(x+2.5)
1.67x+ 4.175 +1.67x=x^2+2.5x
x^2+ 2.5x - 3.38x - 4.175
x^2- 0.84x - 4.175
Using Almighty formula
x = 42 minutes
x + 2.5 +
0.42 + 2.5 = 2.92 hours
