How long should a 14.7 kW pump work in order to pump out 150 m3 of water from a 200 m deep mine?

Let’s determine what work the pump must do in order to raise water from the depths:

A = m * g * h = 150 m³ * 1000 kg / m³ * 9.8 m / s² * 200 m = 294 000 000 J.

Power is the speed at which work is done, so:

N = A / t, whence t = A / N = 294,000,000 J / 14,700 W = 19,600 s = 5 h 26 min 40 s.

Answer: the pump will pump out water for 5 hours 26 minutes 40 seconds.