Algebra 1

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The first of three pipes fills a tank in 12 minutes and a second pipe in 10 minutes.If both these pipes and also a third pipe are open, the tank is filled in 4 minutes. How many minute will the third pipe alone require to fill the tank?

Just need an equation.
Thank you!

  • Algebra 1 -

    Let tank volume = V in gallons
    First pipe fill rate = Q1 = V/12 g.p.m
    Second pipe fill rate = Q2 = V/10 g.p.m
    Let Q3 = third pipe fill rate in gallons/min

    4 minutes = V/(Q1 + Q2 + Q3)
    = V/(V/12 + V/10 + Q3).
    = 1/(1/12 + 1/10 + Q3/V)

    1/3 + 2/5 + 4 Q3/V = 1
    4 Q3/V = 4/15
    Q3/V = 1/15
    Fill time with pipe 3 alone = V/Q3 = 15 minutes

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