Question
Mark partially drained his pool to clean it. At 1:00 P.M., he started to refill it. At 5:00 P.M., the pool had 10,400 gallons of water. At 9:00 P.M., the pool had 13,800 gallons of water. If filling the pool is modeled by a linear function, how many gallons of water still remained in the pool when he first started to refill it?
Responses
A 6,1506,150
B 6,5006,500
C 7,0007,000
D 7,150
Responses
A 6,1506,150
B 6,5006,500
C 7,0007,000
D 7,150
Answers
GPT-4o mini
To solve this problem, we will first determine the rate at which the pool is being filled and then use that to find the initial amount of water in the pool when Mark started to refill it.
Given:
- At 5:00 P.M. (4 hours after starting), the pool had 10,400 gallons.
- At 9:00 P.M. (8 hours after starting), the pool had 13,800 gallons.
1. **Calculate the increase in water between 5:00 P.M. and 9:00 P.M.**:
- Increase = 13,800 gallons - 10,400 gallons = 3,400 gallons
- This increase happened over 4 hours (from 5:00 P.M. to 9:00 P.M.).
2. **Calculate the rate of filling**:
- Rate = Increase / Time = 3,400 gallons / 4 hours = 850 gallons per hour.
3. **Determine the amount of time that had passed since refilling began**:
- From 1:00 P.M. to 5:00 P.M., 4 hours passed.
4. **Calculate the total amount of water in the pool at 1:00 P.M.**:
- In those 4 hours, the pool would have filled:
- Water added = Rate * Time = 850 gallons/hour * 4 hours = 3,400 gallons.
- Therefore, at 1:00 P.M. (when refilling started), the amount of water in the pool was:
- 10,400 gallons - 3,400 gallons = 7,000 gallons.
Thus, the amount of water that remained in the pool when he first started to refill it is **7,000 gallons**.
The correct response is **C 7,000**.
Given:
- At 5:00 P.M. (4 hours after starting), the pool had 10,400 gallons.
- At 9:00 P.M. (8 hours after starting), the pool had 13,800 gallons.
1. **Calculate the increase in water between 5:00 P.M. and 9:00 P.M.**:
- Increase = 13,800 gallons - 10,400 gallons = 3,400 gallons
- This increase happened over 4 hours (from 5:00 P.M. to 9:00 P.M.).
2. **Calculate the rate of filling**:
- Rate = Increase / Time = 3,400 gallons / 4 hours = 850 gallons per hour.
3. **Determine the amount of time that had passed since refilling began**:
- From 1:00 P.M. to 5:00 P.M., 4 hours passed.
4. **Calculate the total amount of water in the pool at 1:00 P.M.**:
- In those 4 hours, the pool would have filled:
- Water added = Rate * Time = 850 gallons/hour * 4 hours = 3,400 gallons.
- Therefore, at 1:00 P.M. (when refilling started), the amount of water in the pool was:
- 10,400 gallons - 3,400 gallons = 7,000 gallons.
Thus, the amount of water that remained in the pool when he first started to refill it is **7,000 gallons**.
The correct response is **C 7,000**.