A pipe normally fills a tank in 12 hours, but, due to a leak, it takes 8 hours…

To determine how long the leak takes to empty the tank, we analyze the work rates:

Determine the normal fill rate:
The pipe fills the tank in 12 hours. Therefore, the rate of the pipe is 1/12 of the tank per hour.

Determine the rate with the leak:
The problem states it takes 8 hours more than the normal time due to the leak.
Total time with leak = 12 hours + 8 hours = 20 hours.
Therefore, the combined rate (pipe filling + leak emptying) is 1/20 of the tank per hour.

Calculate the leak rate:
Let the rate of the leak be $L$. Since the leak is emptying the tank, we subtract its rate from the pipe's rate:
(Pipe Rate) - (Leak Rate) = (Combined Rate)
1/12 - L = 1/20

Solve for L:
L = 1/12 - 1/20
To subtract these fractions, find a common denominator (60):
L = 5/60 - 3/60
L = 2/60 = 1/30

Calculate the time:
If the leak empties the tank at a rate of 1/30 per hour, it will take 30 hours to empty the full tank.