A cowboy at a ranch fills a water trough that is 1.1 m long, 62 cm wide, and 48 cm deep. He uses a hose having a diameter of 2.4 cm, and the water emerges from the hose at 2.4 m/s.

Question

How long does it take the cowboy to fill the trough?
Answer in units of s.

Answer 1

Volume tank= 1.1*.62*height
DV/dt= 1.1*.62 dh/dt

Hose: dv/dt= area*velocity

areahose*velocity= 1.1*.62*dh/dt

itegrate over time
areahose*velocity*time= 1.1*.62*h
solve for time.

Answer 2

Volume= l * W *h in meters
Velocity= 2.4 m/s
Area= (pi)(r^2)
Flow rate= Velocity times area
Time= Volume/Flow Rate