A pump can fill a tank in 2 hours. Due to a leak, it takes 2 1/3 hours to fill. In how many hours can the leak alone drain the full tank?

Problem restatementA pump fills a tank in 2 hours, but with a leak present, filling takes 2 1/3 hours. Find the time the leak alone would need to empty a full tank.

Given data

• Pump's fill time (alone) = 2 h ⇒ fill rate = 1/2 tank per hour.
• Fill time with leak = 2 1/3 h = 7/3 h ⇒ net fill rate = 1 ÷ (7/3) = 3/7 tank per hour.

Concept/ApproachNet rate = pump rate − leak rate. Hence leak rate = pump rate − net rate.

Step-by-step calculation Leak rate = 1/2 − 3/7 = (7/14 − 6/14) = 1/14 tank per hour Time for leak alone to drain full tank = 1 ÷ (1/14) = 14 hours

Verification/AlternativeCheck: With leak, net = 1/2 − 1/14 = (7 − 1)/14 = 6/14 = 3/7 tank per hour ⇒ time 7/3 h = 2 1/3 h (matches).

Common pitfalls

• Adding rates instead of subtracting to get the net with a leak (which drains).

Final Answer14 hours