Question

taps X and Y can fill up an Empty tank in 15 and 12 hours respectively another tap Z can empty the full tank in 8 hours if all the taps are turned on together at the same time in how many hours will the tank be half full

Answer 1

how can a tap empty the full tank? (z)

Answer 2

in 1h tap x can filled=1/15 part of the tank
in 1h tap y can filled=1/12 part of the tank
in 1h tap z can filled=1/8 part of the tank

working together=(1/x+1/y)-1/z
                             = (1/15 +1/12) - 1/8
                             =( (12+15)/15x12)-1/8
                            =27/180-1/8
                            =3/20-1/8
                           =( (8x3-20x1)/8x20)
                           =4/160
                          =1/40
                         =40 h
                         the tank will be full in 40 h