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March 29, 2017

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Beginning with a tank containing 8075 gallons of gasoline, more gas is added at a rate of 5 gallons per minute, while alcohol is added at a rate of 10 gallons per minute. When the mixture is 10% alcohol, how many gallons of the mixture are in the tank?

Is there an easier way to do it than writing out every number and making a table, I'm pretty sure there is, but I can't remember it.

  • Math - ,

    An easier way is algebra.
    Beginning at time t=0, the amount of gasoline in the tank In gallons) is
    G = 8075 + 5 t
    and the amount of alcohol is
    A = 10 t.
    The mixture is 10% alcohol when
    A /(G + A) = 0.1 or
    G = 9 A.
    So, solve this equation for t:
    8075 + 5 t = 90 t
    85t = 8075
    t = 95 minutes.

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