When using the big hose and the small hose, Sam can fill her pool in 15 minutes. The small hose when used alone takes 60 minutes to fill the pool. How long would it take Sam to fill her pool using only the big hose?

Don't understand how to set up equation.

in 15 min the small hose fills 1/4 of the pool, while the big hose fills the other 3/4

3/4 in 15 min means 20 min to fill

To solve this problem, we can set up an equation using the concept of work rates.

Let's denote the rate at which Sam can fill the pool using the big hose as R1 (in pools/minute) and the rate at which she can fill the pool using the small hose as R2 (in pools/minute).

We know from the information given in the problem that when Sam uses both the big and small hose, she can fill the pool in 15 minutes. So, the combined rate at which they fill the pool is 1 pool/15 minutes, which we can write as 1/15 (in pools/minute).

The work rate formula states that the combined rate is equal to the sum of the individual rates. Therefore, we have the equation:

R1 + R2 = 1/15

We also know that when Sam uses only the small hose, it takes her 60 minutes to fill the pool. So, the rate at which she fills the pool using the small hose alone is 1 pool/60 minutes, which is 1/60 (in pools/minute).

Now, we can substitute the values into the equation:

R1 + 1/60 = 1/15

To find the value of R1, we can simplify the equation:

R1 = 1/15 - 1/60

To subtract the fractions, we need a common denominator, which is 60. Therefore, we have:

R1 = (4 - 1)/60
= 3/60
= 1/20

So, Sam can fill her pool using only the big hose at a rate of 1/20 pools per minute.

To determine how long it would take Sam to fill her pool using only the big hose, we can take the reciprocal of the rate:

1 / (1/20) = 20

Hence, it would take Sam 20 minutes to fill her pool using only the big hose.