SOLUTION: It takes red 9 hours longer than Hannah to build a stone wall. Working together, they can build the wall in 20 hours. How long would it take each, working alone, to build the wall?
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Question 782510: It takes red 9 hours longer than Hannah to build a stone wall. Working together, they can build the wall in 20 hours. How long would it take each, working alone, to build the wall? Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! let Hannah take x hours
she does 1/x of job in 1 hour
Red takes x+9 hours
so he does 1/(x+9) of the job in 1 hour
In 1 hour they do
of the job in 1 hour
=1/20
multiply by 20x(x+9)
20(x+9)+20x=x(x+9)
20x+180+20x=x^2+9x
x^2+9x-40x-180=0
x^2-31x-180=0
x^2-36x+5x-180=0
x(x-36)+5(x-36)=0
(x-36)(x+5)=0
x=36 OR x=-5
ignore negative
Hannah does it in 36 hours
Red does it 45 hours (36+9)
