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
Dec 4, 2016

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 #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#