SOLUTION: A roofer and assistant can repair a roof working together in 6 hours. Working alone the assistant can complete the repair in 14 hours. If the roofer and the assistant work togeth

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Question 257142: A roofer and assistant can repair a roof working together in 6 hours. Working alone the assistant can complete the repair in 14 hours. If the roofer and the assistant work together for 2 hours, and then the assistant is left alone to complete the job, how many more hours should the assistant need to finish the repairs?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A roofer and assistant can repair a roof working together in 6 hours.
Working alone the assistant can complete the repair in 14 hours.
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Let x = time required by the roofer working alone (required to do the next part)
:
Let the completed job = 1
:
6%2Fx + 6%2F14 = 1
Multiply by 14x
14(6) + 6x = 14x
84 = 14x - 6x
84 = 8x
x = 84%2F8
x = 10.5 hrs, roofer working alone
:
If the roofer and the assistant work together for 2 hours, and then the assistant is left alone to complete the job, how many more hours should the assistant need to finish the repairs?
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Let a = additional hrs required by the assistant working alone
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Let the completed job = 1
:
2%2F10.5 + %28a%2B2%29%2F14 = 1
Multiply equation by 147 (10.5*14)
2(14) + 10.5(a+2) = 147
28 + 10.5a + 21 = 147
10.5a + 49 = 147
10.5a = 147 - 49
10.5a = 98
a = 98%2F10.5
a = 91%2F3 more hrs for assistant to finish the job
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Prove this with a calc
2/10.5 + 11.33/14 = 1.00