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21 March, 18:11

Work Rate One worker can complete a task in h hours while a second can complete the task in 3h hours. Show that by working together they can complete the task in t = 3/4h hours.

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  1. 21 March, 20:32
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    Answer: t = (3/4) h hours.

    Therefore, it takes both of them (3/4) h hours to complete the task.

    Step-by-step explanation:

    Let

    t1 represent the time taken for the one worker to complete a task.

    t2 represent the time taken for the second worker to complete a task

    And t represent the time taken for both.

    t1 = h

    t2 = 3h

    Let x represent the task.

    x = rate * time

    r1, r2 and r are the rates at which first, second and both worker works

    x = r1 (t1) ... 1

    x = r2 (t2) ... 2

    x = r (t) ... 3

    And,

    r = r1 + r2. (Rate of both equals sum of rates of the two)

    From eqn 1 and 2

    r1 = x/t1 = x/h

    r2 = x/t2 = x/3h

    r = r1 + r2 = x/h + x/3h = 4x/3h

    Substituting r = 4x/3h into equation 3

    x = r (t)

    x = (4x/3h) t

    Making t the subject of formula

    t = x / (4x/3h)

    t = 1 / (4/3h)

    t = 3h/4

    t = (3/4) h hours.

    Therefore, it takes both of them (3/4) h hours to complete the task.
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