One pipe fills a water tank 3 times faster than the other. If the two pipes together can fill the empty tank in 37 minutes, then how much time will the slower pipe alone take to fill the tank?

Given:

Let the time taken by the slower pipe to fill the tank be T minutes.

Then, the time taken by the faster pipe to fill the tank will be T / 3 minutes (since the faster pipe fills 3 times faster).

Calculation:

The rate of the slower pipe = 1 / T (portion of the tank filled per minute).

The rate of the faster pipe = 3 / T (portion of the tank filled per minute).

When both pipes are working together, their combined rate is:

1 / T + 3 / T = 1 / 37 (since they can fill the tank in 37 minutes)

1 / T + 3 / T = 1 / 37

⇒ 4 / T = 1 / 37

⇒ T = 4 × 37

⇒ T = 148 minutes

∴ The slower pipe alone will take 148 minutes to fill the tank.