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

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?
A. 2/3
B. 1
C. 3/4
D. 3/2
E. 2







In 1 hr,
1/c - (1/a + 1/b)  = -2/3 part of tank empty.
Hence:
Hr Empty part
1 2/3
x 1/2 (We know tank is half full)
x = 3/4