Question

A pump can fill a tank in 2 hours. Because of a leak, it took \( 2 \frac{1}{3} \) hours (or 7/3 hours) to fill the tank. In how many hours can the leak drain all the water?

• A. 14 hours
• B. 7/3 hours
• C. 3/7 hours
• D. 7 hours

Hint:

When combining rates, always remember to subtract the draining rate from the filling rate.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Let the filling rate of the pump be \( P \) and the draining rate of the leak be \( L \). The tank capacity is 1 unit.

Step 2: Key Formula or Approach:
Filling rate \( P = 1/2 \) tank/hour.
Net rate with leak \( P - L = 1 / (7/3) = 3/7 \) tank/hour.

Step 3: Detailed Explanation:
\[ \frac{1}{2} - L = \frac{3}{7} \]
\[ L = \frac{1}{2} - \frac{3}{7} = \frac{7 - 6}{14} = \frac{1}{14} \text{ tank/hour} \]
Time taken by leak to drain = \( 1 / L = 14 \) hours.

Step 4: Final Answer:
The leak can drain the tank in 14 hours.