Question

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

• A. 24 hours
• B. 36 hours
• C. 48 hours
• D. Never fills

Hint:

For pipes with opposing actions, calculate the net rate by subtracting the emptying rate from the filling rate, then find the reciprocal for total time.

Answer 1

The Correct Option is A

- Step 1: Rate of filling pipe = $\dfrac{1}{6}$ tank per hour; rate of emptying pipe = $-\dfrac{1}{8}$ tank per hour.
- Step 2: Net rate when both are open = $\dfrac{1}{6} - \dfrac{1}{8} = \dfrac{4 - 3}{24} = \dfrac{1}{24}$ tank per hour.
- Step 3: Time to fill the tank = $\dfrac{1}{\dfrac{1}{24}} = 24$ hours.
- Step 4: Verify: In 24 hours, filling pipe fills $24 \times \dfrac{1}{6} = 4$ tanks; emptying pipe empties $24 \times \dfrac{1}{8} = 3$ tanks. Net = $4 - 3 = 1$ tank.
- Step 5: Check options: Option (a) is 24 hours, which matches.
- Step 6: Note: If net rate were negative, the tank would never fill, but here it is positive.