Final answer:
The unit rate of 3/4 gallon per 1/2 minute equates to 1.5 gallons per minute after simplification. To convert gallons to quarts, the number of gallons is multiplied by the conversion factor of 4 quarts per gallon.
Step-by-step explanation:
To match the unit rate to its ratio, we first need to understand what each of these terms means. A unit rate is a comparison of two measurements where one of the values is 1. For example, 55 miles per hour (55 miles/1 hour) is a unit rate. The given unit rate in the question, 3/4 gallon per 1/2 minute, can be simplified by finding how much of a gallon would be used in one full minute. To do this, we multiply both sides of the ratio by 2 (since there are 2 halves in a whole), which gives us 3/2 gallons per minute or 1.5 gallons per minute.
To solve a conversion problem, such as figuring out how many quarts are in a specific number of gallons, we use the conversion factor that there are 4 quarts in a gallon. Therefore, if we need to convert gallons to quarts, we multiply the number of gallons by 4. For example, converting 8(1/2) gallons to quarts, we calculate 8.5 gallons x 4 = 34 quarts.