Pipe A can fill a tank in 36 minutes and Pipe B can empty the tank in 45 minutes. If both the pipes are opened simultaneously, then the time (in hours) to fill the tank to half of its capacity is:

Pipe A can fill a tank in 36 minutes and Pipe B can empty the tank in 45 minutes.

LCM of 36 and 45 = 180.

Let's assume the total capacity of the tank is 180 units.

The efficiency of Pipe A = $$\frac{180}{36}$$

= 5 units/minute

The efficiency of Pipe B = $$\frac{180}{45}$$

= -4 units/minute (Here negative sign represents that the pipe is used to empty the tank.)

If both the pipes are opened simultaneously, then the time is taken to fill the tank to half of its capacity = $$\frac{\frac{1}{2}\times\ 180}{\left(5-4\right)}$$

= 90 minutes

= $$\frac{90}{60}$$ hours

= 1.5 hours