Answer:
If both the inlet pipe and the outlet pipe are left open, the vat will never completely fill. This is because the outlet pipe is draining the beer from the vat at a faster rate than the inlet pipe is filling it.
To understand why, let's break it down. The inlet pipe can fill the vat in 60 minutes, which means it can fill 1/60th of the vat's capacity every minute. On the other hand, the outlet pipe can drain a full vat in 80 minutes, which means it can drain 1/80th of the vat's capacity every minute.
When both pipes are open, the net rate at which the vat is being filled is the difference between the rate at which the inlet pipe fills it and the rate at which the outlet pipe drains it. In this case, the net rate is 1/60 - 1/80 = 1/240 of the vat's capacity per minute.
Since the net rate is positive, the vat is filling, but at a very slow rate. It will never completely fill because the outlet pipe is continuously draining some of the beer. In other words, the rate at which the beer is being drained is greater than the rate at which it is being filled.
Therefore, the vat will never be completely filled if both the inlet pipe and the outlet pipe are left open.
Explanation: