Question

Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.

Let x be the number of minutes water has been added.

(a)
For each pool, write an expression for the amount of water in the pool after x minutes.
Amount of water in the first pool (in liters) = ____
Amount of water in the second pool (in liters) = ____


(b)
Write an equation to show when the two pools would have the same amount of water.

______________

Answer 1

Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute.

Let x be the number of minutes water has been added.

(a)

For each pool, write an expression for the amount of water in the pool after x minutes.

Amount of water in the first pool (in liters) = 23x + 728

Amount of water in the second pool (in liters) = 37x

(b)

Write an equation to show when the two pools would have the same amount of water.

this is when:

23x + 728 = 37x

subtract 23x from both sides:

23x + 728 - 23x = 37x - 23x

728 = 14x

divide both sides by 14:

728/14 = 14x/14

x = 52

So, pools are equal after 52 minutes.