SOLUTION: 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 long would it take the faster roofer working alone?

Question 1167923: 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 long would it take the faster roofer working alone?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = quantity.

let x = the rate of the slower roofer.

then 3x = the rate of the faster roofer.

when they work together their rates are additive and they can roof a house in 5 days.

quantity = 1 roof

formula becomes:

(x + 3x) * 5 = 1
combine like terms to get:
4x * 5 = 1
simplify to get:
20x = 1
solve for x to get:
x = 1/20

that's the rate of the slower roofer.

the rate of the roofer is 3 times that = 3/20 of the job per day.

when the faster roofer is working alone, the equation becomes:

3/20 * time = 1

solve for time to get:

time = 20/3

the faster roofer, working alone, can roof a house in 20/3 days.

that would be 6 and 2/3 days.

that should be your answer. *****

to go a few steps further, .....

when the slower roofer works alone, the formula becomes:

1/20 * time = 1

solve for time to get:

time = 20 days.

the faster roofer completes the job in 6 and 2/3 days, working alone.
the slower roofer completes the job in 20 days, working alone.

it takes the slower work 3 times as long to complete the job as the faster worker.

that's because the faster worker is 3 times as fast as the slower worker.

everything checks out.

your solution is good.

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