darlingriyarai wrote:Pumps A, B, and C each work at their own constant rate. When a certain tank is full, it takes pump A, operating alone, 3 hours to empty the tank; and it takes pump B, operating alone, 2 hours to empty the full tank. When the tank is empty, it takes pump C, operating alone, 6 hours to fill the tank. If all 3 pumps operate simultaneously, with pumps A and B emptying the tank and pump C filling it, how many minutes will it take to empty the tank if it is initially 1/2 full?
A. 30
B. 35
C. 40
D. 45
E. 50
Let the tank = 6 units.
Rate for Pump A to empty the tank = w/t = 6/3 = 2 units per hour.
Rate for Pump B to empty the tank = w/t = 6/2 = 3 units per hour.
Rate for Pump C to fill the tank = w/t = 6/6 = 1 unit per hour.
Combined rate for all 3 pumps = 2+3-1 = 4 units per hour.
Half the tank = 3 units.
Time for all 3 pumps to empty half the tank = w/r = 3/4 hours = 45 minutes.
The correct answer is
D.
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