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)

Question

Responses

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.

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.

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.

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

Answer 1

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

1. Understanding the equation:

   • \( x \) represents the number of miles between the shop and the delivery location.
   • \( y \) represents the total time in minutes from when an order is placed until it is delivered.
   • The equation indicates that the delivery time consists of two parts: a constant preparation time of 5 minutes (the y-intercept) and a variable travel time that depends on the distance (the term \( 2.5x \)).

2. Breaking down the components:

   • The constant term (5 minutes) reflects the average preparation time for food.
   • The coefficient of \( x \) (which is 2.5) represents the delivery time per mile. Therefore, it takes 2.5 minutes to travel 1 mile.

Now, let's evaluate the statements based on the model:

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

   • This is incorrect. The delivery time is 2.5 minutes per mile, not 5 miles per minute.

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

   • This is also incorrect. The delivery person travels 1 mile in 2.5 minutes, not 2.5 miles in 1 minute.

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

   • This is incorrect. It takes 2.5 minutes to travel 1 mile, not 5 minutes.

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

   • This is incorrect. The preparation time is represented by the constant term of 5 minutes.

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

   • This statement is correct. This matches our understanding of how the equation represents travel time.

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

   • This statement is correct. This is directly indicated by the y-intercept of the equation.

Correct Statements:

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