SOLUTION: Two pools are being filled with water. To start, the first pool contains 823 liters of water and the second pool contains 1300 liters of water. Water is being added to the

Question 1104694: Two pools are being filled with water. To start, the first pool contains
823
liters of water and the second pool contains
1300
liters of water. Water is being added to the first pool at a rate of
35.75
liters per minute. Water is being added to the second pool at a rate of
22.5
liters per minute.
full answer please!!!!!!!!!
1.after how many minutes will the two pools have the same amount of water?
2.how much water will be in the pool when they have the same amount?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let,
x = number of minutes that have elapsed

The first pool contains 823 liters of water. Water is being added to the first pool at a trate of 35.75 liters per minute. So after x minutes, the first pool will have a total of 35.75*x+823 liters of water
The quantity 35.75*x represents the additional amount of water added after those x minutes go by, which is added on top of the 823 liters already there.

Similarly, the second pool will have a total of 22.5*x+1300 liters since it starts off with 1300 liters and we add on 22.5*x additional liters from the hose.

If we want to know when the two pools are filled with the same amount of water, we set the expressions equal to each other and solve for x
Amount of water for pool 1 = Amount of water for pool 2
35.75*x+823 = 22.5*x+1300
35.75*x+823-823 = 22.5*x+1300-823
35.75*x = 22.5*x+477
35.75*x-22.5*x = 22.5*x+477-22.5*x
13.25*x = 477
13.25*x/13.25 = 477/13.25
x = 36

After 36 minutes, the two pools will have the same amount of water.

Plug x = 36 into either expression to get the amount of water
Amount of water for pool 1 = 35.75*x+823
Amount of water for pool 1 = 35.75*36+823
Amount of water for pool 1 = 1287+823
Amount of water for pool 1 = 2110
OR
Amount of water for pool 2 = 22.5*x+1300
Amount of water for pool 2 = 22.5*36+1300
Amount of water for pool 2 = 810+1300
Amount of water for pool 2 = 2110

Technically you only have to pick one equation, but its good practice to use both to confirm we have the right answer.
-----------------------------------------------------
-----------------------------------------------------
Now to answer the two questions:
Question 1: After how many minutes will the two pools have the same amount of water?
Answer 1: 36 minutes
-------
Question 2: How much water will be in the pool when they have the same amount?
Answer 2: 2110 liters (this is the amount for each pool; not the combined from both pools)

RELATED QUESTIONS
Two pools are being filled with water. To start, the first pool contains 823 liters... (answered by josgarithmetic)

Please put final answer Two pools are being filled with water. To start, the first... (answered by ankor@dixie-net.com)

Two pools are being filled with water. To start, the first pool contains 980 liters of... (answered by Boreal)

Two pools are being filled with water. (answered by ikleyn)

Isabella filled her pool with water at a constant rate. The table compares the remaining (answered by ikleyn)

The isosceles triangle pool is 20ft height and 35ft base. The equilateral triangle pool... (answered by ikleyn,fractalier)

A swimming pool holds 600,000 liters of water. The pool has two drainage pipes. When the (answered by 303795)

Please help... A swimming pool holds 540,000 liters of water. The pool has two drainage... (answered by ptaylor,josmiceli)

A swimming pool holds 540,000 liters of water. THe pool has two drainage pipes. When the... (answered by mananth)