Question

paul can finish building a house 4 weeks longer than cesar can build one.if they both work together,they can build a house in 4.8 weeks.how fast can cesar build a house alone

Answer 1

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? 

..

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 

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