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?

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

idk

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