Final answer:
To verify if the fountain sprayed at the same rate, we analyze the volume of water and the time it ran. By calculating the volume per hour, we find that the fountain consistently sprayed at a rate of 30 gallons per hour when it was on.
Step-by-step explanation:
To determine if the fountain sprayed water at the same rate during both periods it was on, we need to consider the volume of water sprayed and the time it was running. The first time, the fountain sprayed 20 gallons over the course of an hour. The second time, it sprayed 30 gallons in half an hour. To find the rate, we divide the volume of water sprayed by the time. For the first period: rate = 20 gallons / 1 hour = 20 gallons per hour. For the second period: rate = 30 gallons / 0.5 hours = 60 gallons per hour. However, to compare the rates directly, we need to convert the second rate to the same time unit as the first. Therefore, we divide 60 gallons per hour by 2 (since a half hour is half of an hour), and we get 30 gallons per hour. This shows that the fountain sprayed water at the same rate of 30 gallons per hour during the times it was on.