If it takes two roofers 4 hours to put a new roof on a portable classroom. If the first roofer can do the job by himself in 12 hours, how many hours will second roofer to do the job by himself?
It would take 6 hours for the other person to complete the roof on there own.
This is the sort of situation where you have to get used to 'enumerating' effort. For example: 1 roof's worth of work.
Let the work rate per hour of roofer 1 be
Let the work rate per hour of roofer 2 be
Standardise the total amount of work needed by the unit of: 1 roof
Initial condition: They both work together for 4 hours to complete the building of 1 roof
We are also told that
So his work rate
Using Equation(2) substitute for
Multiply both sides by 6
So it would take 6 hours for the other person to complete the roof on there own.