Question

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?

Answer 1

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 `W_1`
Let the work rate per hour of roofer 2 be`W_2`

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

`4W_1+4W_2=1`roof....................................Equation(1)

We are also told that `" "12W_1=1 larr` 12 hours of work for 1 roof
So his work rate `(W_1)` is `1/12` roof per hour

So

`W_1=1/12`roof .................................................Equation(2)

Using Equation(2) substitute for `W_1` in Equation(1) giving:

`4(1/12"roof")+4W_2=1"roof "............Equation(1_a)`
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`(1/3"roof")+4W_2=1" roof"`

`4W_2=1"roof" - 1/3"roof"`

`4W_2=2/3"roof"`

`=>W_2=2/3xx1/4 = 1/6` of a roof per hour

Remember that `W_2` is the work rate for that person

Multiply both sides by 6

`W_2=1/6"roof"" "->" "6xxW_2=(6xx1/6)" roof"`

`6W_2=1"roof"`

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

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`color(blue)("Check")`

`(4xx1/12) + (4xx1/6) = 1/3+2/3=1`