Question

A​ cold-water faucet can fill a sink in 1212 ​min, and a​ hot-water faucet can fill it in 1515 min. The drain can empty the sink in 2525 min. If both faucets are on and the drain is​ open, how long will it take to fill the​ sink?

Answer 1

Answer:

9.1 minutes.

Step-by-step explanation:

Let t represent time taken to fill the tank.

We have been given that a cold water faucet can fill a sink in 12 ​min, so the part of sink filed in 1 minute would be $\frac{1}{12}$.

The hot-water faucet can fill it in 15 min, so the part of sink filed in 1 minute would be $\frac{1}{15}$.

The drain can empty the sink in 25 min, so the part of drain emptied in 1 minute would be $\frac{1}{25}$.

The part of 1 full tank filled in t minutes, when both faucets are on and the drain is​ open would be:

$(\frac{1}{12}+\frac{1}{15}-\frac{1}{25})t=1$

Make a common denominator:

$(\frac{1*25}{12*25}+\frac{1*20}{15*20}-\frac{1*12}{25*12})t=1$

$(\frac{25}{300}+\frac{20}{300}-\frac{12}{300})t=1$

$(\frac{25+20-12}{300})t=1$

$\frac{33}{300}t=1$

$\frac{11}{100}t=1$

$\frac{100}{11}\times \frac{11}{100}t=\frac{100}{11}\times1$

$t=\frac{100}{11}$

$t=9.0909$

$t\approx 9.1$

Therefore, it will take 9.1 minutes to fill the sink.