Question 557367
rate x time = work

Fill rate = 1/10
Time = x
Work = 1/10 * x = x/10

Drain rate = 1/12
Time = x
Work = 1/12 * x = x/12

x/10 - x/12 = 1
LCM = 60
60(x/10 - x/12 = 1)
6x - 5x = 60
x = 60

It will take 60 minutes or 1 hour to fill the tub with water.