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 3.9 minutes. If both faucets are open, the sink is filled in 3 minutes. How long does it take to fill the sink with just the hot water faucet open?

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 3.9 minutes. If both faucets are open, the sink is filled in 3 minutes. How long does it take to fill the sink with just the hot water faucet open?

Answer:

It'll take 13 minutes to fill the sink with only the hot water faucet open.

 

 

Analysis

Given that the sink can be filled by:

 Cold water faucet= 3.9 minutes

Both faucets= 3 minutes

We can add the rates of filling to get rate of filling together

Let “t+” = time in minutes for the hot water faucet to fill sink

Therefore, the rate for hot water faucet can be expressed as:

[1 sink filled] / [3.9 min] (where 1 sink filled] / [t min]

1/t + 1/3.9 = 1/3

Multiply both sides by 3.3.9.t

3.3.9. t = 3.9.t

11.7t=.9t

t=13

Hence4, it will take 13 minutes for the hot water faucet to fill sink