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

First, determine the individual filling rates of the two pipes.
Pipe A fills the tank in 1 hour, so its rate is $1$ tank/hour.
Pipe B fills the tank in $1 \frac{1}{2} = \frac{3}{2}$ hours.
So, the rate of Pipe B = $\frac{1}{\frac{3}{2}} = \frac{2}{3}$ tank/hour.
Now, when both pipes are opened together, their rates are added:
Combined rate = $1 + \frac{2}{3} = \frac{5}{3}$ tanks/hour.
This means together, they fill $\frac{5}{3}$ of a tank every hour.
Now, to find the time to fill one full tank:
\[ \text{Time} = \frac{1}{\frac{5}{3}} = \frac{3}{5} \text{ hours} \]
Convert hours to minutes: $\frac{3}{5} \times 60 = 36$ minutes.
Hence, both pipes together can fill the tank in 36 minutes.