Question

problems 3–8: charlie filled up the tub and gave the family dog a bath. then charlie let the water in the tub drain. the graph shows the amount of water in the tub, in gallons, as a function of time, in minutes.

1. label the axes.
2. when did charlie turn off the water faucet?
3. how much water was in the tub when charlie bathed the dog?
4. how long did it take the tub to drain completely?

at what rate did the faucet fill the tub?
at what rate did the water drain from the tub?

Explanation:

Step1: Label axes (given context)

Vertical axis: Gallons (Water in Tub)
Horizontal axis: Time (Minutes)

Step2: Find faucet off time

Look for when water stops increasing. The flat segment starts at 6 minutes.

Step3: Find bath water amount

The flat segment has a constant value of 18 gallons.

Step4: Calculate drain time

Drain starts at 18 mins, ends at 30 mins. $30 - 18 = 12$ minutes.

Step5: Calculate fill rate

Fill 18 gallons in 6 mins. $\frac{18}{6} = 3$ gallons/minute

Step6: Calculate drain rate

Drain 18 gallons in 12 mins. $\frac{18}{12} = 1.5$ gallons/minute

Answer:

1. Vertical Axis: Gallons (Amount of Water in Tub); Horizontal Axis: Time (Minutes)
2. At 6 minutes
3. 18 gallons
4. 12 minutes
5. 3 gallons per minute
6. 1.5 gallons per minute