Question

A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both are opened together, how long will it take to fill the tank?

• A. 12 hours
• B. 24 hours
• C. 36 hours
• D. 48 hours

Hint:

For pipes, combine rates (positive for filling, negative for emptying) to find net rate.

Answer 1

The Correct Option is B

- Step 1: Filling pipe rate = $\frac{1}{6}$ tank/hour, emptying pipe rate = $-\frac{1}{8}$ tank/hour.
- Step 2: Net rate = $\frac{1}{6} - \frac{1}{8} = \frac{4 - 3}{24} = \frac{1}{24}$ tank/hour.
- Step 3: Time to fill = $\frac{1}{\text{Net rate}} = \frac{1}{\frac{1}{24}} = 24$ hours.
- Step 4: Verify: In 24 hours, filling pipe fills $24 \times \frac{1}{6} = 4$ tanks, emptying pipe empties $24 \times \frac{1}{8} = 3$ tanks, net = 1 tank.
- Step 5: Option (2) is 24 hours, correct.