Atank can be filled by one pump in 50 minutes and by another pump in 60 minutes. a third pump can drain the tank in 75 minutes. if all 3 pumps go into operation, how long will it take to fill the tank?

42 6/7 minutes

Step-by-step explanation:

Each minute, the first pump adds 1/50 of a tank; the second pump adds 1/60 of a tank; and the third pump subtracts 1/75 of a tank. Then, each minute the total amount added is ...

... (1/50) + (1/60) - (1/75) = 6/300 + 5/300 - 4/300

... = 7/300 . . . . of a tank.

Then in 300/7 minutes, or 42 6/7 minutes, the tank will be full.

the answer to the expression is 83