To analyze the situation, we can look at how the amount of water in the tank decreases over time according to the given table:
- At 4 hours: 1,190 gallons
- At 8 hours: 1,180 gallons
- At 12 hours: 1,170 gallons
- At 16 hours: 1,160 gallons
From the data, we can calculate the amount of water lost over time:
- From 4 to 8 hours: 1,190 - 1,180 = 10 gallons lost in 4 hours
- From 8 to 12 hours: 1,180 - 1,170 = 10 gallons lost in 4 hours
- From 12 to 16 hours: 1,170 - 1,160 = 10 gallons lost in 4 hours
Thus, the constant leak rate is \( \frac{10 \text{ gallons}}{4 \text{ hours}} = 2.5 \text{ gallons/hour} \).
Next, we determine the initial amount of water in the tank. The tank started with 1,190 gallons at 0 hours; thus, it appears the tank is gradually leaking from this initial amount.
Based on this analysis, let's review the options:
A. The tank initially had 1,190 gallons of water, which is leaking at the rate of 5 gallons per hour. (Incorrect: Rate is 2.5 gallons/hour)
B. The tank initially had 1,190 gallons of water, which is leaking at the rate of 10 gallons per hour. (Incorrect: Rate is 2.5 gallons/hour)
C. The tank initially had 1,200 gallons of water, which is leaking at the rate of 5 gallons per hour. (Incorrect initial amount and rate)
D. The tank initially had 1,200 gallons of water, which is leaking at the rate of 2.5 gallons per hour. (Incorrect initial amount)
Given that the original water amount matches the water at 0 hours indicating it would be 1,190 gallons, we conclude:
The correct choice is: A. The tank initially had 1,190 gallons of water, which is leaking at the rate of 2.5 gallons per hour.
However, none of the provided choices exactly match this conclusion. The problem could potentially contain a misrepresentation in the options offered.
2 answers