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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=2.5x+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.(2 points)
Responses

The average amount of time the shop needs to prepare the food for delivery is 5 minutes.
The average amount of time the shop needs to prepare the food for delivery is 5 minutes.

On average, the delivery person travels 5 miles every 1 minute.
On average, the delivery person travels 5 miles every 1 minute.

The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.
The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.

On average, the delivery person travels 2.5 miles every 1 minute.
On average, the delivery person travels 2.5 miles every 1 minute.

On average, it takes the delivery person 5 minutes to travel 1 mile.
On average, it takes the delivery person 5 minutes to travel 1 mile.

On average, it takes the delivery person 2.5 minutes to travel 1 mile.
On average, it takes the delivery person 2.5 minutes to travel 1 mile.

1 answer

To analyze the equation \( y = 2.5x + 5 \):

  • y represents the total time in minutes from when the order is placed until it is delivered.
  • x represents the number of miles between the shop and the delivery location.

From the equation:

  1. The constant term 5 indicates that there is a fixed preparation time of 5 minutes before the delivery person starts travelling. Therefore, we can conclude that:

    • The average amount of time the shop needs to prepare the food for delivery is 5 minutes. (This is true.)

  2. The coefficient 2.5 before x indicates that for every additional mile, it takes an extra 2.5 minutes to deliver. Thus, if we consider the travel time per mile:

    • On average, it takes the delivery person 2.5 minutes to travel 1 mile. (This is also true.)

With that analysis, the two correct statements according to the model are:

  1. The average amount of time the shop needs to prepare the food for delivery is 5 minutes.
  2. On average, it takes the delivery person 2.5 minutes to travel 1 mile.