A medium water hose can fill a pool in 30 minutes. A larger water hose can fill the same pool in 20 minutes. If both hoses are turned on at the same time, how long will it take to fill the pool?
-What equation can be used to solve this work problem?

-How many minutes will it take both hoses to fill the pool?

Step-by-step explanation: Given that a medium water hose can fill a pool in 30 minutes and a larger water hose can fill the same pool in 20 minutes.

We are to find the number of minutes they will take to fill the pool if both hoses are turned on at the same time.

Let, 't' be the time taken to fill the pool if both the hoses are turned on at the same time.

We have,

Time taken by the medium hose to fill the pool = 30 minutes.

So, in 1 minute, the part of the pool filled by the medium hose will be

[tex]\dfrac{1}{30}.[/tex]

And,

Time taken by the larger hose to fill the pool = 20 minutes.

So, in 1 minute, the part of the pool filled by the larger hose will be

[tex]\dfrac{1}{20}.[/tex]

Therefore, in 1 minute, the part of the pool filled by both the hoses is

[tex]\dfrac{1}{30}+\dfrac{1}{20}.[/tex]

Now, time taken by both the hoses to fill the pool = t minutes.

So, in 1 minute, the part of the pool filled by both the hoses is

[tex]\dfrac{1}{t}.[/tex]

Hence, we must have

[tex]\dfrac{1}{30}+\dfrac{1}{20}=\dfrac{1}{t}\\\\\\\Rightarrow \dfrac{5}{60}=\dfrac{1}{t}\\\\\\\Rightarrow \dfrac{1}{12}=\dfrac{1}{t}\\\\\\\Rightarrow t=12.[/tex]

Thus, the required equation is

[tex]\dfrac{1}{30}+\dfrac{1}{20}=\dfrac{1}{t}[/tex] and the time taken by both the hoses to fill the pool is 12 minutes.