A sandwich shop makes home deliveries. The average amount of time from when an order is placed until it is delivered can be modeled by the equation y = 2.5 + 5, where x is the number of miles between the shop and the delivery location and y is the time in minutes. Which of these statements are correct according to the model?
Select TWO that apply.
A. On average, the delivery person travels 5 miles every 1 minute.
B. On average, the delivery person travels 2.5 miles every 1 minute.
C. On average, it takes the delivery person 5 minutes to travel 1 mile.
D. The average amount of time the shop needs to prepare the food for delivery is 5 minutes.
E. On average, it takes the delivery person 2.5 minutes to travel 1 mile.
F. The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.
The equation given to model the average amount of time from when an order is placed until it is delivered is y = 2.5 + 5x. Note that there seems to be a slight typo in the presentation of the equation; normally, the x would follow the 5 to denote its dependence on the number of miles. The correct equation should be y = 2.5 + 5x.
Based on this corrected equation, the following statements can be interpreted:
A. On average, the delivery person travels 5 miles every 1 minute. (Incorrect. The equation shows that each mile adds 5 minutes to the delivery time, not the other way around.)
B. On average, the delivery person travels 2.5 miles every 1 minute. (Incorrect. There's no data provided on speed, and the 2.5 in the equation is an initial value, not a rate of travel.)
C. On average, it takes the delivery person 5 minutes to travel 1 mile. (Correct. The rate of time per mile in the equation is 5 minutes per mile.)
D. The average amount of time the shop needs to prepare the food for delivery is 5 minutes. (Incorrect. The equation denotes the constant term 2.5 as the initial time, not 5.)
E. On average, it takes the delivery person 2.5 minutes to travel 1 mile. (Incorrect. This contradicts the rate of 5 minutes per mile given by the equation.)
F. The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes. (Correct. The equation y = 2.5 + 5x includes a constant term, 2.5, which is the starting value for y when x is zero, indicating an initial time value before any delivery distance is considered, likely the prep time.)
Therefore, the correct statements according to the given equation are:
C. On average, it takes the delivery person 5 minutes to travel 1 mile.
F. The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.