Question

A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold water faucet in 3 minutes. If both faucets are open, the sink is filled in 2 minutes. How long does it take to fill the sink with just the hot water faucet open?

Answer 1

Answer: $6\ minutes$

Step-by-step explanation:

You can use the following formula:

$\frac{T}{A}+\frac{T}{B}=1$

You can say that "T" is the time (in minutes) for both faucets working together, "A" is the time (in minutes) for cold water faucet working alone and "B" is the time (in minutes) for hot water faucet working alone.

Based on the data given in the exercise, you can identify that:

$T=2\\A=3$

Therefore, substituting these values into the formula and solving for "B", you get that this is:

$\frac{2}{3}+\frac{2}{B}=1\\\\\frac{2}{B}=1-\frac{2}{3}\\\\\frac{2}{B}=\frac{1}{3}\\\\2=\frac{1}{3}B\\\\2*3=B\\\\B=6$