Question

Pipe A can fill a tank in 1 hour and Pipe B can fill it in $1\frac{1}{2}$ hours. If both the pipes are opened in the empty tank, how much time will they take to fill the tank?

Hint:

Work and time problems often require rate conversion. Always find individual rates, then add them to find combined rate for joint work.

Answer 1

Determine the filling rate of each pipe individually. Pipe A's rate is 1 tank/hour as it fills the tank in 1 hour. Pipe B fills the tank in $1 \frac{1}{2} = \frac{3}{2}$ hours, so its rate is $\frac{1}{\frac{3}{2}} = \frac{2}{3}$ tank/hour. When both pipes operate simultaneously, their rates combine: Combined rate = $1 + \frac{2}{3} = \frac{5}{3}$ tanks/hour. This signifies that together, they fill $\frac{5}{3}$ of a tank per hour. To calculate the time required to fill one full tank, use the formula: \[\text{Time} = \frac{1}{\frac{5}{3}} = \frac{3}{5} \text{ hours}\]Convert this duration to minutes: $\frac{3}{5} \times 60 = 36$ minutes. Therefore, the tank will be filled in 36 minutes when both pipes are open.