The cold water faucet can fill a sink in 2 minutes. The drain can empty a full sink in 3 minutes. If the faucet were left on and the drain was left open, how long would it take to fill the sink?

6 minutes

Step-by-step explanation:

Let the volume of the sink be Xm^3

The rate of filling the sink by the first faucet is R1 while the rate of draining the faucet is - R2 (negative since it's draining)

R1 = x/2

R2 = - x/3 (negative as it is draining)

The time it would take both of them working at the same rate to fill the sink is as follows:

x / (R1 - R2) = T

x / (x/2 - x/3) = T

x = T (x/2 - x/3)

x = T ((3x - 2x) / 6)

x = T (x/6)

x = Tx/6

6x = Tx

T = 6 minutes