Question

Pipe A can fill a tank in 30 hours and pipe B in 45 hour. If both the pipes are opened in an empty tank how much time will they take to fill it?

Answer 1

18 hours

===========

Determine the combined rate at which they fill the tank.

Let's denote the rate at which pipe A fills the tank as a, and the rate at which pipe B fills the tank as b.

Given that pipe A can fill the tank in 30 hours, we have:

• a = 1/30 (tank per hour)

Similarly, pipe B can fill the tank in 45 hours, so we have:

• b = 1/45 (tank per hour)

When both pipes are open, their rates add up, so the combined rate at which they fill the tank is given by:

• a + b =
• (1/30) + (1/45) =
• (3/90) + (2/90) =
• 5/90 (tank per hour)

To find the time it will take to fill the tank, we need to invert the combined rate.

So the tank will be filled in:

• 90/5 = 18 hours