Question

(a) a train travels from city a to city b. the table below shows the distance and the amount of time it takes on the train.

distance (in kilometers)	6	15	21

choose the correct description.

• the train does not always go the same distance each minute.
• the train appears to go the same distance each minute.

predicted distance traveled in 8 minutes: \\(\square\\) km

(b) leila is deciding how many people to take to the movies. the table below shows the cost for

Explanation:

Part (a)

Step 1: Calculate the speed (distance per minute) for each data point

To find the distance per minute, we use the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).

• For the first data point: Distance = 6 km, Time = 2 minutes.

Speed \( = \frac{6}{2} = 3 \) km per minute.

• For the second data point: Distance = 15 km, Time = 5 minutes.

Speed \( = \frac{15}{5} = 3 \) km per minute.

• For the third data point: Distance = 21 km, Time = 7 minutes.

Speed \( = \frac{21}{7} = 3 \) km per minute.

Step 2: Analyze the speed

Since the speed (distance per minute) is 3 km/min for all three data points, the train appears to go the same distance each minute.

Step 3: Predict the distance for 8 minutes

Using the speed of 3 km per minute, we calculate the distance for 8 minutes using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \).

Distance \( = 3 \times 8 = 24 \) km.

Final Answers for (a)

• Correct description: The train appears to go the same distance each minute.
• Predicted distance in 8 minutes: \( \boldsymbol{24} \) km.

(Note: For part (b), the problem statement is incomplete. Please provide the full table or details for part (b) to solve it.)

Answer:

Part (a)

Step 1: Calculate the speed (distance per minute) for each data point

To find the distance per minute, we use the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).

• For the first data point: Distance = 6 km, Time = 2 minutes.

Speed \( = \frac{6}{2} = 3 \) km per minute.

• For the second data point: Distance = 15 km, Time = 5 minutes.

Speed \( = \frac{15}{5} = 3 \) km per minute.

• For the third data point: Distance = 21 km, Time = 7 minutes.

Speed \( = \frac{21}{7} = 3 \) km per minute.

Step 2: Analyze the speed

Since the speed (distance per minute) is 3 km/min for all three data points, the train appears to go the same distance each minute.

Step 3: Predict the distance for 8 minutes

Using the speed of 3 km per minute, we calculate the distance for 8 minutes using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \).

Distance \( = 3 \times 8 = 24 \) km.

Final Answers for (a)

• Correct description: The train appears to go the same distance each minute.
• Predicted distance in 8 minutes: \( \boldsymbol{24} \) km.

(Note: For part (b), the problem statement is incomplete. Please provide the full table or details for part (b) to solve it.)