Question 1167923
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.