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Math Help - Why do this?

  1. #1
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    Why do this?

    A tank was being filled with water at the rate of 1.5 gallons/minute. By 10 A.M., it contained 50 gallons. Several minutes later, the water going into the tank was turned off, the plug was pulled, and the tank was drained at a rate of 2.3 gallons/minute. The tank was empty at 11:08 A.M. How many minutes did it take to drain the tank?

    I know 50+1.5x=2.3(68-x) where x is the time in min after 10 that the tank fills, but why must these be equal.

    LHS is the amount in the tank after x minutes and RHS is the amount that leaves the tank after x minutes.
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  2. #2
    Member Furyan's Avatar
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    Re: Why do this?

    Hello

    They must be equal so you can solve for x and find how many minutes the tank took to drain. They are equal because the volume of water in the tank when it is full is the same as the volume of water that drains out of it to make it empty.

    The LHS is the amount of water in the tank x minutes after 10:00 am and the RHS is the amount that drains out of the tank in (68-x) minutes.
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