**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 \(B\) = \(\frac{1}{B} = \frac{1}{9}\)

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.

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

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

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