SOLUTION: Alex and Bobby work together to primer their master�s fence. This takes them thirty minutes. If they had to work alone, Alex would take twenty-five minutes more to paint their se

Question 408348: Alex and Bobby work together to primer their master�s fence. This takes them thirty minutes. If they had to work alone, Alex would take twenty-five minutes more to paint their sensei�s fence than Bobby would take. How long would it take Alex to paint their master�s fence if working alone? Please make sure to clearly define any variables you use, and write your final answer in the form of a complete sentence with appropriate units.
Thank you,

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Alex and Bobby work together to primer their master�s fence. This takes them thirty minutes. If they had to work alone, Alex would take twenty-five minutes more to paint their sensei�s fence than Bobby would take. How long would it take Alex to paint their master�s fence if working alone? Please make sure to clearly define any variables you use, and write your final answer in the form of a complete sentence with appropriate units.
..
let x=minutes alex would take to complete the job working alone.
Therefore, 1/x=Alex's minute work rate.
Bobby would take x-25 minutes to complete the job working alone.
Therefore,1/(x-25)=Bobby's minute work rate.
They would take 30 minutes to complete the job working together.
Therefore, 1/30 would be their minute work rate working together.
The sum of the individual work rates=work rate working together.
(1/x)+1/(x-25)=1/30
LCD=x(x-25)(30)
30x-750+30x=x^2-25x
x^2-85x+750=0
(x-10)(x-75)=0
x=10(this answer is not possible, so it is rejected)
x=75
ans:
It would take Alex 75 minutes to complete the job working alone.
It would take Bobby 50 minutes to complete the job working alone.

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