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.
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Let x = time required by the roofer working alone (required to do the next part)
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Let the completed job = 1
:
{{{6/x}}} + {{{6/14}}} = 1 
Multiply by 14x
14(6) + 6x = 14x
84 = 14x - 6x
84 = 8x
x = {{{84/8}}}
x = 10.5 hrs, roofer working alone
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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
:
{{{2/10.5}}} + {{{(a+2)/14}}} = 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 = {{{98/10.5}}}
a = 9{{{1/3}}} 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