Final answer:
Harry incorrectly calculated a unit rate of pounds per quart as gallons per quart. The correct unit rate is 1/40 gallons per quart, based on conversion factors between ounces, pounds, and gallons. Harry's error was likely in not correctly applying the conversion of 16 ounces in a pound and 128 ounces in a gallon.
Step-by-step explanation:
The correct unit rate that Harry is trying to calculate should convert pounds to gallons, keeping quarts constant, since he is looking for a rate in 'gallons per quart'. We know that there are 16 ounces in 1 pound, and there are 4 quarts in 1 gallon. To find the correct unit rate, we need to use conversion factors.
First, we convert Harry's initial rate of 1/5 pounds per 1/120 quart to more standard units. Since there are 16 ounces in a pound, we convert pounds to ounces:
- (1/5 pound) * (16 ounces/pound) = 16/5 ounces
To convert ounces to gallons, we notice that Harry's likely error was that he did not account for the customary liquid conversion of pounds to gallons correctly. Since 1 gallon equals 4 quarts and there are 32 ounces in one quart (as 2 pints = 1 quart and 2 cups = 1 pint and 8 ounces = 1 cup; hence, 8 ounces * 4 = 32 ounces), we can find the number of ounces in a gallon:
- (32 ounces/quart) * (4 quarts/gallon) = 128 ounces/gallon
Thus, we can determine the amount of gallons per quart:
- (16/5 ounces) / (128 ounces/gallon) = (16/5) / (128) = 1/40 gallons per quart
In conclusion, the correct unit rate is 1/40 gallons per quart, not 1/100 as Harry incorrectly believed.