Filling the tank

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A tank has three taps. The first can fill the tank in 4 hours, the second can fill the tank in 2 hours and the third can empty the tank in 8 hours. How long will it take to fill the tank with all three taps operating at the same time? (You can assume the tank is empty to begin with).


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It will take 1 hour 36 mins to fill the tank.
In one hour the fraction, or portion, of the tank filled will be:
1/4 + 1/2 – 1/8 = 5/8
If 5/8 takes 60 mins, then 1/8 takes 12 mins, and 8/8 = 96 minutes

 

3 thoughts on “Filling the tank

  1. 1:36 minutes is the correct answer, but let me fully explain it for anyone that is having trouble:

    TapA can fill in 4 hours (ie: TapA=Hour/4 to fill)
    TapB can fill in 2 hours (ie: TapB=Hour/2 to fill)
    TapC emptys the tank in 8 hours (ie: TapC=Hour/8 to empty)
    So our formula is 1=TapA+TapB-TapC
    which then becomes 1=h/4+h/2-h/8
    Now we need a common denominator to make this easier. 4,2 and 8 call all use the denominator 8, so our new formula becomes:
    1=(2h/(4*2))+(4h/(2*4)-(1h/8*1)
    simplified that becomes: 1=(2h)/8+(4h)/8-h/8
    simplified again becomes: 1=5h/8
    multiply our denominator makes: 8=5h
    divide by to get our variable alone makes: 8/5=h
    8/5 of an hour is 1 and 3/5hour or 1hour and 36 minutes.

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