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One roofer can put a new roof on a house three times faster than another. Working together they can roof a house in 5 days. How
many days would it take the faster roofer to put a new roof on a house working alone? Round the answer to the nearest tenth.

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sqdancefan

Answer:

  6.7 days

Step-by-step explanation:

If t is the time the faster roofer takes, then the slower one takes 3t. Their combined rates in roofs per day are ...

  1/t + 1/(3t) = 1/5

  4/(3t) = 1/5 . . . . . . combine terms

  t = 5(4/3) = 20/3 ≈ 6.7 . . . . multiply by 5t

The faster roofer working alone can roof a house in about 6.7 days.