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

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.

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

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

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

1 answer

To analyze the equation \( y = 2.5x + 5 \), where \( x \) is the number of miles and \( y \) is the total time in minutes from when an order is placed until it is delivered, we can break down the components:

  1. The 5 minutes: This represents the constant time taken irrespective of the distance, which can be interpreted as the fixed time required to prepare the food for delivery.

  2. The 2.5x term: This represents the time taken for the delivery person to travel, where \( 2.5 \) is the time in minutes it takes to travel each mile. So, it takes the delivery person 2.5 minutes to travel 1 mile.

Based on this analysis, the 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." (This is indicated by the constant in the equation.)

  2. "On average, it takes the delivery person 2.5 minutes to travel 1 mile." (This is indicated by the coefficient of \( x \) in the equation.)

Therefore, the two correct statements are:

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