SOLUTION: one roofer can put a new roof on a house three times faster than another. Working together, they can roof a house in 4 days. How long would it take the faster roofer working alone?

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Question 250438: one roofer can put a new roof on a house three times faster than another. Working together, they can roof a house in 4 days. How long would it take the faster roofer working alone?
Answer by chosenpoint(26) About Me  (Show Source):
You can put this solution on YOUR website!

Rate-of-work-word-problems/250438 (2009-12-15 21:54:41): one roofer can put a new roof on a house three times faster than another. Working together, they can roof a house in 4 days. How long would it take the faster roofer working alone?

Let x be the fastest roofers time to roof the house

Then the slower roofers time will be 3x

Use the following formula to calculate how the work is done:

1%2FA%2B1%2FB=1%2FC where A & B are the times done by themselves, and C is the time it takes them to do the work together, thus we have:

1%2Fx%2B1%2F3x=1%2F4

3%2F3x%2B1%2F3x%2B1%2F4

4%2F3x=1%2F4

3x=16

x=16%2F3

So the fast roofer can do it by himself in about 5.33 days! Hope that helps! :)