Two pools are being filled with water. To start, the first pool contains 1660 liters of water and the second pool contains 1900 liters of water. Water is being added to the first pool at a rate of 30.75 liters per minute. Water is being added to the second pool at a rate of 23.25 liters per minute.

How much water will be in each pool when they have the same amount

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.

Step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is