Final answer:
The faucet leaked at a rate of 1/2 gallon per hour. This was calculated by taking the amount of water leaked, 1/4 of a gallon, for the time frame of 1/2 an hour, and adjusting it to a per hour rate.
Step-by-step explanation:
To determine the leak rate of the faucet in gallons per hour, we need to first take note of the amount of water leaked in the given time frame. The faucet leaked 1/4 of a gallon of water in 1/2 of an hour. To find the rate per hour, we perform the following calculation:
Gallons per hour = Gallons leaked / Time in hours
Gallons per hour = (1/4) / (1/2)
Since we are looking for a rate per one hour, we need to adjust for the fact that the leak occurred over only half an hour. Therefore, we multiply the leaked amount by 2 (since there are two halves in a whole), which gives us:
Gallons per hour = (1/4) * 2/1 = 2/4 = 1/2 gallon per hour.