At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?  Answers:
A) 2 / 3 B) 1 C) 3 / 4 D) 3 / 2 E) 2

Rationale: rate of a = 1 / 2 tank / hour ; rate of b = 1 / 3 tank / hour ; rate of c = 1 / 6 tank / hour . combined rate when a and b are used to pump - out water , while c is used to fill water into the tank is 1 / 2 + 1 / 3 - 1 / 6 = 2 / 3 tank hour . so , to empty the full tank 3 / 2 hours ( reciprocal of rate ) are needed . to empty the half - full tank half of that time would be needed : 1 / 2 * 3 / 2 = 3 / 4 hours . answer : c .
Answer: C