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**HallsofIvy** Pipe A is running at a rate of 1/36 "cistern pre minute". Pipe B is running at a rate of 1/48 "cistern per minute" so while they are both running they are filling the cistern at (1/36+ 1/48)= 1/(6*6)+ 1/(8*6)= 4/144+ 3/144= 7/144 "cistern per minute". If they both run for t minutes, they will fill 7x/144 of the cistern. If A only runs for 24- t minutes, it will fill another (24- t)/36 so that to fill the entire cistern will be filed in 7t/144+ (24- t)/36= (7t+ 4(24- t))/144= (3t+ 96)/144= t. Solve that equation for t.