My textbook gives the following word problem:
Henry and Irene working together can wash all the windows of their house in 1h 48m. Working alone, it takes Henry 1.5h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
I know the answer is 3 and 4.5, but I don't know how they arrived at this. Here is what I do know and have done:
1h 48m = 1.8h
Irene's work time: x
Henry's work time: x + 1.5
Working together: 1/x + 1/(x+1.5) = 1/1.8
I've multiplied through by 1.8x(x+1.5) to eliminate the denominators and ended up with the following:
1.8(x+1.5) + 1.8x = x(x+1.5)
1.8x + 2.7 + 1.8x = x[sup:32ih4xpe]2[/sup:32ih4xpe]+1.5x
3.6x +2.7 = x[sup:32ih4xpe]2[/sup:32ih4xpe]+1.5x
x[sup:32ih4xpe]2[/sup:32ih4xpe]-2.1x-2.7=0
This is where I lose it. I've used the quadratic formula to solve for x but I get x =2.31. What am I doing wrong?
Thank you.
Henry and Irene working together can wash all the windows of their house in 1h 48m. Working alone, it takes Henry 1.5h more than Irene to do the job. How long does it take each person working alone to wash all the windows?
I know the answer is 3 and 4.5, but I don't know how they arrived at this. Here is what I do know and have done:
1h 48m = 1.8h
Irene's work time: x
Henry's work time: x + 1.5
Working together: 1/x + 1/(x+1.5) = 1/1.8
I've multiplied through by 1.8x(x+1.5) to eliminate the denominators and ended up with the following:
1.8(x+1.5) + 1.8x = x(x+1.5)
1.8x + 2.7 + 1.8x = x[sup:32ih4xpe]2[/sup:32ih4xpe]+1.5x
3.6x +2.7 = x[sup:32ih4xpe]2[/sup:32ih4xpe]+1.5x
x[sup:32ih4xpe]2[/sup:32ih4xpe]-2.1x-2.7=0
This is where I lose it. I've used the quadratic formula to solve for x but I get x =2.31. What am I doing wrong?
Thank you.