A pipe can fill a tank in 1 1/2 hours and another pipe can empty it in 1 3/4 hours. In how much time will the tank be half filled?

The time needed to fill the tank is 3/2 hours, so its fill rate is 2/3 of a tank per hour.
The time needed to drain the tank is 7/4 hours, so its emptying rate is 4/7 of a tank per hour.

I assume you start with an empty tank and turn on both pipes. The net rate of filling is therefore:
2/3 - 4/7 of a tank per hour

You want to know how many hours until it is half filled.
(2/3 - 4/7)t = 1/2

Multiply both sides by the common denominator of 42:
42(2/3 - 4/7)t = 42(1/2)
(28 - 24)t = 21
4t = 21
t = 21/4
t = 5 1/4

Answer:
5 1/4 hours