Final answer:
The rate of 20 4/5 gallons every 1/4 hour converts to a unit rate of 83.2 gallons per hour by multiplying the rate per 1/4 hour by 4, giving us 416/5, which simplifies to 83.2 gallons per hour.
Step-by-step explanation:
The student asked to express the rate of filling a pool at 20 4/5 gallons every 1/4 hour as a unit rate. A unit rate is the rate for one unit of a given quantity. To find the unit rate, we must determine how many gallons are filled in one hour. Since there are four quarters in one hour, we multiply the rate per 1/4 hour by 4 to find the number of gallons filled in one hour.
First, convert 20 4/5 to an improper fraction: 20 × 5 + 4 = 104/5. Then multiply by 4:
104/5 × 4/1 = 416/5 gallons per hour.
Next, simplify the fraction by dividing 416 by 5:
416 ÷ 5 = 83.2 gallons per hour.
This is the unit rate, giving us 83.2 gallons per hour as the rate at which the pool is being filled.