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    Topics || Problems

    A tank has one supply pipe in which could fill the tank in 5 hours and another which could fill it in 9 hours. How many hours will it take to fill the tank if both pipes are used simultaneously?

    Let \(A\) be the number of hours in which the fist pipe can fill the tank alone.
    Rate of \(A\) = \(\frac{1}{A} = \frac{1}{5}\)
    Let \(B\) be the number of hours which the second pipe can fill the tank alone.
    Rate of \(B\) = \(\frac{1}{B} = \frac{1}{9}\)

    If both pipe work together: \( \frac{1}{A} + \frac{1}{B} = \frac{1}{T}\), where \(T\) is the total number of hours the two pipes can fill the tank.

    \(\frac{1}{5} + \frac{1}{9} = \frac{1}{T}\)

    \(\frac{9+5}{45} = \frac{1}{T}\)

    \(T = \frac{45}{14} \approx 3.21 ~ hours\)