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:
Rate of work: If a pump fills in \( t \) hours, its rate is \( 1/t \). Let the leak drain the tank in \( L \) hours (rate = \( -1/L \)).

Step 2: Detailed Explanation:
Rate of pump = \( 1/2 \).
Combined rate = \( \frac{1}{7/3} = 3/7 \).
Rate of pump - Rate of leak = Combined rate
\( 1/2 - 1/L = 3/7 \).
\( 1/L = 1/2 - 3/7 = (7-6)/14 = 1/14 \).
\( L = 14 \).

Step 3: Final Answer:
The leak can drain the tank in 14 hours.