Question

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

• A. 18 hours
• B. 24 hours
• C. 30 hours
• D. 36 hours

Hint:

Always treat filling as positive and emptying as negative when adding rates for combined work problems.

Answer 1

The Correct Option is B

- Step 1: Rate of filling pipe - The first pipe fills 1 tank in 6 hours, so its rate is: \[ \frac{1}{6} \ \text{tanks/hour} \] 
- Step 2: Rate of emptying pipe - The second pipe empties 1 tank in 8 hours, so its rate is: \[ -\frac{1}{8} \ \text{tanks/hour} \] 
- Step 3: Net rate when both are open - \[ \frac{1}{6} - \frac{1}{8} = \frac{4 - 3}{24} = \frac{1}{24} \ \text{tanks/hour} \] 
- Step 4: Time to fill 1 tank - Since rate × time = 1 tank: \[ \frac{1}{24} \times T = 1 \implies T = 24 \ \text{hours} \] 
- Step 5: Conclusion - It will take 24 hours, matching option (2).