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11 March, 10:11

A pond is being drained through an outlet pipe, then will be filled through an inlet pipe. If the inlet pipe can fill the pond in 9 hours and the outlet pipe can empty the pond in 15 hours, how long would it take to fill the pond if the outlet pipe was left open?

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  1. 11 March, 10:38
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    22.5 hours

    Step-by-step explanation:

    I am using "1 pond" to mean the volume of water that fits in the pond.

    The inlet pipe fills the pond in 9 hours.

    The filling rate is (1 pond) / (9 hours) = 1/9 pond/hour

    The outlet pipe empties the pond in 15 hours.

    The emptying rate is (1 pond) / (15 hours) = 1/15 pond per hour

    The difference in rates is the net rate at which the pond is filling up.

    1/9 pond/hour - 1/15 pond/hour =

    = 5/45 pond/hour - 3/45 pond / hour

    = 2/45 pond/hour

    The pond is filling at a rate of 2/45 pond/hour.

    To find the time it takes to fill the pond, we divide 1 pond by the rate.

    (1 pond) / (2/45 pond/hour) = 45/2 hour = 22.5 hours
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