Question

Two containers are being filled with water. One begins with 8 gallons of water and is filled at a rate of 3.5 gallons per minute. The other begins with 24 gallons and is filled at 3.25 gallons per minute.

Part A: Write an equation that represents the amount of water =w, in gallons, with respect to time =t, in minutes, for each container.

Part B: Solve the system of equations. Show your work.

Part C: How long would it take for both of the containers to have the same amount of water? How much water would be in each container?

Answer 1

After 64 minutes the tanks will have the same amount of water.

After 64 minutes the tanks will have 232 gallons of water

Explanation:

Part A.

We propose the equation for the first container. We call t the time in minutes that tank 1 takes to fill up and we call w the amount of water that tank 1 has as a function of time.

The tank starts with 8 gallons and every minute it fills 3.5 gallons more.

Then the equation is:

`w = 3.5t + 8`

We propose the equation for the second container. We call t the time in minutes that tank 2 takes to fill and we call w the amount of water that tank 2 has as a function of time.

The tank starts with 24 gallons and every minute it fills 3.25 gallons more.

Then the equation is:

`w = 3.25t + 24`

Part B

Now re.solvemos the system

`w = 3.5t + 8` (i)

`w = 3.25t + 24` (ii)

Now we introduce (i) in (ii)

`3.5t + 8 = 3.25t + 24`

`0.25t = 16`

`t = (16)/(0.25)`

`t = 64\ min\\\\w = 3.5(64) +8\\\\w = 232\ gallons`

Part C.

After 64 minutes the tanks will have the same amount of water.

After 64 minutes the tanks will have 232 gallons of water