Question

A pipe fills a tank in 4 hours; another empties it in 8 hours. If both are opened, how long will it take to fill the tank?

• A. 4 hours
• B. 6 hours
• C. 8 hours
• D. 10 hours

Hint:

In pipes and cisterns, subtract rates if one pipe empties the tank.

Answer 1

The Correct Option is C

To solve this problem, we need to understand how the two pipes work together to fill the tank. We have two pipes:

1. Pipe A, which can fill the tank in 4 hours.
2. Pipe B, which can empty the tank in 8 hours.

Let's calculate the rate at which each pipe works:

• The rate of Pipe A is \(\frac{1}{4}\) of the tank per hour (since it fills the tank in 4 hours).
• The rate of Pipe B is \(-\frac{1}{8}\) of the tank per hour (since it empties the tank in 8 hours).

When both pipes are opened together, their rates are combined. The net rate of filling the tank is given by:

\[\text{Net rate} = \frac{1}{4} - \frac{1}{8}\]

To calculate the net rate, find a common denominator:

\[\text{Net rate} = \frac{2}{8} - \frac{1}{8} = \frac{1}{8}\]

This means that both pipes together fill \(\frac{1}{8}\) of the tank in one hour.

Therefore, it will take 8 hours to fill the whole tank when both pipes are open, because:

\[\text{Time} = \frac{1 \text{ whole tank}}{\frac{1}{8} \text{ of the tank per hour}} = 8 \text{ hours}\]

Thus, the correct answer is 8 hours.