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March 28, 2017

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A certain toilet tank can be emptied in 6 sec through its drain when it is flushed. This happens at the same time that the water is flowing in through the inlet pipe. Withthe drain closed, the inlet pipe canfill the tank in 30 sec. How long would it take to drain the tank if the water was not flowingin through the inlet pipe?

  • algebra - ,

    in flow rate Q1 = 1 tank / 30 seconds
    out flow rate = Q2

    Q2 - Q1 = 1 tank/6 seconds

    Q2 - 1/30 = 1/6
    Q2 = 5/30 + 1/30 = 6/30 = 1/5 = 1 tank/5 seconds
    so
    5 seconds

  • algebra - ,

    let the tank hold 1 unit of volume

    let the rate of water flowing in be y units/sec
    let the water flowing out be x units / sec

    When drain is open (water going in and out at the same time)
    6(x-y) = 1
    x - y = 1/6

    drain closed: 30y = 1
    y = 1/30

    plug back into x-y = 1/6
    x - (1/30) = 1/6
    x = 1/5


    only drain open:
    t(1/5) = 1
    t = 5 sec

    With the drain only,
    it would take 5 seconds to empty the tank

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