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?

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

After 64 minutes the tanks will have 232 gallons of water

Step-by-step 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:

 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:

Part B

Now re.solvemos the system

 (i)

  (ii)

Now we introduce (i) in (ii)

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

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places