water going into a pool

Question

Two pools are being filled with water. To start, the first pool had 1950 liters of water and the second pool had 1430 liters of water. Water is being added to the first pool at a rate of 33 liters per minute. Water is being added to the second pool at a rate of 43 liters per minute.

how is the amount of water the same

Answer 1

When do they have the same amount of water can be shown as the intersection between y=1950+33x and y=1430+43x. To find the intersection, we set them equal to each other. That means 1950+33x=1430+43x.

1950+33x=1430+43x

First let's bring the constants to one side.

1950-1430+33x=1430-1430+43x

This leaves us 520+33x=43x.

Next we bring the variables to one side like so

520+33x-33x=43x-33x

With that we have 520=10x.

Divide by the coefficient of x and we get 520/10=10x/10 or x=52. They will have equal amounts of water 52 minutes after they begin to fill.