SOLUTION: A roofer and an assistant can repair a roof tegether in 6 hours. The assistant can complete the repairalone in 14 hhours. If both the roofer and the assistant work together for 2 h

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Question 1011341: A roofer and an assistant can repair a roof tegether in 6 hours. The assistant can complete the repairalone in 14 hhours. If both the roofer and the assistant work together for 2 hours and then the assistant is left alone to finish the job. How much longer will the assistant need to finish the repair?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
RT=J to relate work rate, time, amount of job

First examine their rates, as 1 job per quantity of time in hours
Roofer             1/14

Assistant          1/x

Both together      1/6

1%2F14%2B1%2Fx=1%2F6
2%2A3%2A7x%2F14%2B2%2A3%2A7x%2Fx=2%2A3%2A7%2Ax%2F6
3x%2B42=7x
4x=42
2x=21
x=21%2F2 or 10&1/2.
You can use this rate as highlight_green%281%2Fx=2%2F21%29.

Next, the work to be done is cut into two time periods using different arrangements of roofer and assistant. Let t be the time asked for.
-
highlight%28%281%2F6%292%2B%282%2F21%29t=1%29.
Important is this equation make sense and the earlier rate analysis make sense. Now just solve for t.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A roofer and an assistant can repair a roof tegether in 6 hours. The assistant can complete the repairalone in 14 hhours. If both the roofer and the assistant work together for 2 hours and then the assistant is left alone to finish the job. How much longer will the assistant need to finish the repair?
Assistant takes: highlight_green%289%261%2F3%29 additional hours to complete remaining 2%2F3 of job



Also view problem # 623056, as it's EXACTLY the same problem, but with different numbers.