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?

PART A:

w-3.5 t=8

w-3.25t=24

PART B:

t=64

and w= 232

PART C:

It will take 64 minutes for both of the containers to have the same amount of water.

The amount of water in each container is:

232 gallons.

Step-by-step explanation:

PART A:

Let the water is filling in 't' minutes.

and 'w' denotes the amount of water in the container.

for container 1:

One begins with 8 gallons of water and is filled at a rate of 3.5 gallons per minute.

The equation is given by:

or

for container 2:

The other begins with 24 gallons and is filled at 3.25 gallons per minute.

The equation is given by:

or

PART B:

on solving equation (1) and equation (2) by method of elimination we get:

subtract equation (2) by equation (1) to obtain:

t=64

and  putting the value of t in equation (1) to obtain:

w= 232

PART C:

Hence it will take 64 minutes for both of the containers to have the same amount of water.

The amount of water in each container is:

232 gallons.

-6 is the correct option from the above given options

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80