Question

A swimming pool holds 11,500 gallons of water at the start of the day. A valve at the bottom of the pool releases water into a cleaning tank at a constant rate of 40 gallons per hour. A hose is running water into the pool at a constant rate of 50 gallons per hour. On one day, the hose was running for 5 hours, and the valve was left open for 8 hours. How much water is in the pool at the end of the day?

a) 10,500 gallons
b) 12,000 gallons
c) 13,500 gallons
d) 14,000 gallons

Answer 1

After calculating the net water lost from the pool, there will be 11,430 gallons of water in the pool at the end of the day, which does not match the answer choices provided.

Step-by-step explanation:

To determine how much water is in the pool at the end of the day, we need to calculate the net amount of water added or removed from the pool during that day. The hose adds water at a rate of 50 gallons per hour and was running for 5 hours, while the valve releases water at a rate of 40 gallons per hour and was open for 8 hours.

• Water added by the hose: 50 gallons/hour × 5 hours = 250 gallons
• Water released by the valve: 40 gallons/hour × 8 hours = 320 gallons

Net water lost: 320 gallons – 250 gallons = 70 gallons

Starting with 11,500 gallons and subtracting the net water lost: 11,500 gallons – 70 gallons = 11,430 gallons

Therefore, there will be 11,430 gallons of water in the pool at the end of the day, which is not one of the options provided. It looks like there might be an error in the options given.