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5 July, 11:20

The cold water faucet can fill a sink in 2 minutes. The drain can empty a full sink in 3 minutes. If the faucet were left on and the drain was left open, how long would it take to fill the sink?

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  1. 5 July, 12:12
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    6 minutes

    Step-by-step explanation:

    Let the volume of the sink be Xm^3

    The rate of filling the sink by the first faucet is R1 while the rate of draining the faucet is - R2 (negative since it's draining)

    R1 = x/2

    R2 = - x/3 (negative as it is draining)

    The time it would take both of them working at the same rate to fill the sink is as follows:

    x / (R1 - R2) = T

    x / (x/2 - x/3) = T

    x = T (x/2 - x/3)

    x = T ((3x - 2x) / 6)

    x = T (x/6)

    x = Tx/6

    6x = Tx

    T = 6 minutes
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