Water enters a 4.00-m3 tank at a rate of 6.33 kg/s and is withdrawn at a rate of 3.25 kg/s. the tank is initially half full.
repeat the calculation for the time until overflow for the case of water entering a 4.00-m3 tank at a rate of 6.83 kg/s and withdrawn at a rate of 3.50 kg/s. the tank is initially two thirds full.

(a) The time until overflow is 649 s

(b) The time until overflow is 355 s

Explanation:

The volume as a function of time can be expressed as

If the tank is initially half full, V(0) = V0 = 4/2 = 2 m3.

With ρ=1000 kg/m3, the volume flows are

Flow in = 6.33 kg/s * 0.001 m3/kg = 0.00633 m3/s

Flow out = 3.25 kg/s * 0.001 m3/kg = 0.00325 m3/s

The time until overflow (V(t)=4 m3) is

If the flows are

Flow in = 6.83 kg/s * 0.001 m3/kg = 0.00683 m3/s

Flow out = 3.50 kg/s * 0.001 m3/kg = 0.0035 m3/s

And the tank is initially 2/3 full (V(0)=2.67 m3)

The time until overflow is