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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.
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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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