A tank fitted with two pipes is to filled with water. One pipe can fill it in 5 hours. After it has been open for 3 hours, the second pipe is opened and the tank is filled in 4 hours more. How long it would take the second pipe alone to fill the tank?

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  1. let the tank contain V units of volume

    rate of first pipe = V/5 units/hr
    rate of 2nd pipe = V/x units/hr

    So the first pipe runs for 3 hrs
    Volume = 3(V/5) = 3V/5
    the second pipe runs for 4 hrs.
    Volume filled by 2nd pipe = 4(V/x) = 4V/x

    3V/5 + 4V/x = V
    multiply by 5x
    3Vx + 20V = 5xV
    3x + 20 = 5x
    x = 10

    It would take 10 hrs using the 2nd pipe alone

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