SOLUTION: Paul can finish a job in 2 hrs less than John. Working together they can finish it in 2 hours and 24 minutes. How long would it take Paul to finish the job working alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Paul can finish a job in 2 hrs less than John. Working together they can finish it in 2 hours and 24 minutes. How long would it take Paul to finish the job working alone?      Log On


   

Question 358403: Paul can finish a job in 2 hrs less than John. Working together they can finish it in 2 hours and 24 minutes. How long would it take Paul to finish the job working alone?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Paul can finish a job in 2 hrs less than John. Working together they can finish it in 2 hours and 24 minutes. How long would it take Paul to finish the job working alone?
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let john take x hours
he does 1/x of the job in 1 hour.
paul takes x-2 hours
so he does 1/(x-2 ) of the job in 1 hour.
together they do the job in 2 2/5 hours = 12/5 hours
so they do 5/12 of the job in 1 hour.
...
1/x+1/(x-2)=5/12
x-2+x/x(x-2)=5/12
(2x-2)/x(x-2)= 5/12
12(2x-2)=5x(x-2)
24x-24=5x^2-10x
5x^2-10x-24x+24=0
5x^2-34x+24=0
5x^2-30x-4x+24=0
5x(x-6)-4(x-6)=0
(x-6)(5x-4)=0
x=6 x =4/5
...
x= 6 is valid
Paul will take x-2 =4 hours