A 450-gallon tank full of water is draining at a rate of 20 gallons per minute.
a. How many gallons will be in the tank after 7 minutes?
b. How long will it take for the tank to have 200 gallons?
c. Write an equation that represents the relationship between the gallons of water in the tank and minutes the tank has been draining.
d. Graph your equation using graphing technology. Mark the points on the graph that represent the gallons after 7 minutes and the time when the tank has 200 gallons. Write down the coordinates.
e. How long will it take until the tank is empty?

A function show the relationship between an independent variable and a dependent variable. The independent variable (input) does not depend on other variables while the dependent variable (output) depend on other variables.

In this question, amount of water in tank is dependent variable and the time taken is the independent variable. Let y represent amount of water in tank and x represent the time it has been draining. Therefore:

a) This can be represented by the equation:

y = 450 - 20x

At 7 minutes (x = 7)

y = 450 - 20(7)

y = 310 gallons

b) For 200 gallons (y = 200), the time taken is:

200 = 450 - 20x

200 - 450 = -20x

-20x = -250

x = -250/-20

x = 12.5 minutes

c) y = 450 - 20x

d) The graph was plotted using geogebra onling graphing calculator.

e) When the tank is empty, y = 0, hence

0 = 450 - 20x

20x = 450

x = 450 / 20

x = 22.5 minutes

francocanacari francocanacari · Answer 2 · 2025-03-29T18:18:07-04:00

The equation that demonstrates the relationship between the gallons of water in the tank and minutes the tank has been draining is 450 - 20X = Gallons drained. After 7 minutes there will be 310 gallons of water in the tank. It will take 12.5 minutes for the tank to have 200 gallons. It will take 22.5 minutes until the tank is empty.

Since a 450-gallon tank full of water is draining at a rate of 20 gallons per minute, to determine how many gallons will be in the tank after 7 minutes; how long will it take for the tank to have 200 gallons; the relationship between the gallons of water in the tank and minutes the tank has been draining; and how long will it take until the tank is empty, the following calculations must be performed:

The equation that demonstrates the relationship between the gallons of water in the tank and minutes the tank has been draining is 450 - 20X = Gallons drained

450 - (20 x 7) = X
450 - 140 = X
310 = X
Therefore, after 7 minutes there will be 310 gallons of water in the tank.

450 - 20X = 200
450 = 200 + 20X
450 - 200 = 20X
250/20 = X
12.5 = X
Therefore, it will take 12.5 minutes for the tank to have 200 gallons.

450 - 20X = 0
450 = 20X
450/20 = X
22.5 = X
Therefore, it will take 22.5 minutes until the tank is empty.

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