Question

Two large and 1 small pump can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool? Please help me answer I'm in 5th grade and this is so hard.

Answer 1

Let's define.

L = rate at which the large pump fills the pool.

S = rate at which the small pump can fill the pool.

We have two relations:

"Two large and 1 small pump can fill a swimming pool in 4 hours."

(2*L + S)*4h = 1

"One large and 3 small pumps can also fill the same swimming pool in 4 hours."

(L + 3*S)4h = 1

Then we have the system of equations:

(2*L + S)*4h = 1

(L + 3*S)4h = 1

To solve this system, we need to isolate one of the variables in one of the equations, i will isolate S in the first equation:

S = 1/4h - 2*L

Now we can replace that in the second equation:

(L + 3*(1/4h - 2*L))4h = 1

L + (3/4h) - 6*L = 1/4h

-5*L = 1/4h - 3/4h = -2/4h

L = (2/4h)*(1/5) = (2/20h) = 1/10h

This means that one large pump needs 10 hours to fill one pool.

With this, we can find the value of S:

S = 1/4h - 2*L = 1/4h - 2/10h = 5/20h - 4/20h = 1/20h

This means that a small pump needs 20 hours to fill a pool.

Now we can answer:

How many hours will it take 4 large and 4 small pumps to fill the swimming pool?

We need to solve the equation:

(4*(1/10h) + 4*(1/20h))*T = 1

We need to find the value of T.

T = 1/((4*(1/10h) + 4*(1/20h)) = 1.67 hours.

This means that 4 large and 4 small pumps need 1.67 hours to fill a pool.