Question

Also with this one, having to do with proportional relationships

Answer 1

a.
The container starts with 5 gallons.
After 10 minutes it has 3 gallons.
That means that 2 gallons leaked out in 10 minutes.
The rate water is leaking at is (2 gal)/(10 min) = 0.2 gallons per minute

b.
(5 gal)/(0.2 gal/min) = 25 min

The container will be empty 25 minutes after it started leaking.

Answer 2

Part A

After 10 minutes, the container goes from 5 gallons to 3 gallons. So in those 10 minutes, the container loses 2 gallons (5-3 = 2)

Rate = (amount of water lost)/(amount of time elapsed)
Rate = (-2)/(10)
Rate = -1/5
Rate = -0.2

The rate is -0.2 gallons per minute. The negative indicates we have a loss of water. So every minute, the container loses 0.2 gallons (or 1/5 of a gallon). This is the slope. The slope measures rate of change.

Final Answer for part A is 0.2 gallons per minute
In fraction form, the answer would be 1/5 of a gallon per minute

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Part B

The slope found from part A was -0.2, so let m = -0.2
The container initially holds 5 gallons of water, so this is the y intercept. Call this b = 5

Together m = -0.2 and b = 5 will be plugged into y = mx+b to get y = -0.2x+5

The equation y = -0.2x+5 represents how much water is left
x = time in minutes
y = amount of gallons left over

To find out when the container is empty, plug in y = 0 and solve for x
y = -0.2x+5
0 = -0.2x+5
0-5 = -0.2x+5-5
-5 = -0.2x
-0.2x = -5
-0.2x/(-0.2) = -5/(-0.2)
x = 25

It will take 25 minutes for the container to empty

Final Answer to part B: 25 minutes