Question

Two faucets can be used to empty a tank of water. Suppose the tank is full. When both faucets are opened at the same time, the tank takes 2 hours to empty. However, if only one faucet is opened, then Faucet A can empty the tank twice as fast as Faucet B. If only Faucet B is opened, how long does it take to empty a full tank?

Answer 1

Volume of water in the tank = V

Volumetric flow of water through faucet A = Q₁

Volumetric flow of water through faucet B = Q₂

Time taken to empty the tank when only faucet A is open = T₁

V = Q₁T₁

Time taken to empty the tank when only faucet B is open = T₂

Faucet A empties the tank twice as fast as faucet B.

T₂ = 2T₁

V = Q₂T₂

V = Q₂(2T₁)

Time taken to empty the tank when both faucets are open = T = 2 hours

V = (Q₁ + Q₂)T

T₁ = 1.5T

T₁ = (1.5)(2)

T₁ = 3 hours

T₂ = 2T₁

T₂ = (2)(3)

T₂ = 6 hours

Time taken to empty a full tank if only faucet B is opened = 6 hours