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15 July, 04:35

A roofing contractor can shingle a roof in half the time it takes his assistant. Working together, they can shingle the roof in 8 hours. How much time does it take the roofing contractor to finish the job alone

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  1. 15 July, 04:43
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    It will take him 12 hours working alone

    Step-by-step explanation:

    In this question, we are asked to calculate the time in hours it will take a roofing contractor to finish a job alone given the amount of time he and his assistant will finish the roof job.

    We can identify from the question that he works 2 times as fast as his assistant. So let's say he takes x hours, his assistant will take 2x hours

    Now, let's say the span of the roofing work is y meters.

    His rate will be y/x and his assistant will be y/2x while their joint rate will be y/8

    Now if their individual rates are added together, we will have the joint rate

    Mathematically;

    y/x + y/2x = y/8

    y (1/x + 1/2x) = y (1/8)

    1/x + 1/2x = 1/8

    3x/2x^2 = 1/8

    3/2x = 1/8

    2x = 24

    x = 24/2

    x = 12 hours
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