# 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?

##### 1 Answer

It would take 6 hours for the other person to complete the roof on there own.

#### Explanation:

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

So

Using Equation(2) substitute for

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Remember that

Multiply both sides by 6

So it would take 6 hours for the other person to complete the roof on there own.

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