The pipes can fill a cistern in 1.5 hours and 2 hours respectively. A wste pipe can empty a full cistern in 3 hours. If the cisternis empty and all three pipes are opened together, in how many min will the cistern be half full
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Answer Posted / Bhavna Tyagi
To find out when the cistern will be half full, we first determine the combined flow rate of the two filling pipes: (1/1.5) + (1/2) = 7/6 cubic units per hour. The waste pipe empties the cistern in 3 hours, so its flow rate is (1 cubic unit / 3). To find out how long it takes for the cistern to be half full, we need to find the time when the net flow rate of the filling pipes equals half the volume of the cistern. Let x be the number of hours it takes for the cistern to be half full. Then, (7/6 - 1/3)x = 1/2. Solving this equation gives x ≈ 0.55 hours or approximately 33 minutes.
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