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) 16 21 27
time (in minutes) 4 7 9
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 amount of time to travel 30 kilometers: minutes
(b) melissa

Answer:

Part (a) - Choosing the Correct Description

To determine if the train goes the same distance each minute, we calculate the speed (distance per minute) for each data point. Speed is calculated as \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).

• For the first data point: \( \frac{16}{4} = 4 \) km per minute.
• For the second data point: \( \frac{21}{7} = 3 \) km per minute. Wait, that can't be right. Wait, no, wait: 16 km in 4 minutes: \( \frac{16}{4} = 4 \) km/min. 21 km in 7 minutes: \( \frac{21}{7} = 3 \) km/min? Wait, that's a mistake. Wait, no, 21 divided by 7 is 3? Wait, 7 times 3 is 21, yes. But 16 divided by 4 is 4. Wait, that would mean different speeds. But wait, maybe I miscalculated. Wait, 27 km in 9 minutes: \( \frac{27}{9} = 3 \) km/min. Wait, so first is 4, second and third are 3? That can't be. Wait, maybe the table is misread. Wait, the distance is 16, 21, 27; time is 4, 7, 9. Wait, 16/4 = 4, 21/7 = 3, 27/9 = 3. So the first one is 4, others are 3? That would mean the train does not always go the same distance each minute. But wait, maybe I made a mistake. Wait, no, 16 divided by 4 is 4, 21 divided by 7 is 3, 27 divided by 9 is 3. So the speeds are 4, 3, 3. So the train does not always go the same distance each minute? But wait, maybe the table is different. Wait, maybe the time for 16 km is 4 minutes, 21 km is 7 minutes, 27 km is 9 minutes. Wait, 16/4 = 4, 21/7 = 3, 27/9 = 3. So the first speed is 4, others are 3. So the train does not always go the same distance each minute? But that seems odd. Wait, maybe I misread the table. Wait, maybe the distance is 16, 24, 27? No, the table says 21. Wait, maybe the problem has a typo, but assuming the table is correct, let's recalculate. Wait, 16 km in 4 minutes: 4 km per minute. 21 km in 7 minutes: 3 km per minute. 27 km in 9 minutes: 3 km per minute. So the speed changes. But that would mean the first option is correct. But wait, maybe I made a mistake. Wait, no, 16 divided by 4 is 4, 21 divided by 7 is 3, 27 divided by 9 is 3. So the train does not always go the same distance each minute. But wait, maybe the table is 16, 24, 27? No, the user provided 21. So according to the given table, the speeds are 4, 3, 3. So the first option: "The train does not always go the same distance each minute" is correct? But wait, maybe I miscalculated. Wait, 16/4 = 4, 21/7 = 3, 27/9 = 3. So yes, the speed is not constant. So the correct description is "The train does not always go the same distance each minute."

But wait, maybe the table is different. Wait, maybe the time for 16 km is 4 minutes, 21 km is 5.25 minutes? No, the table says 7. Wait, maybe the problem is correct, and I need to check again. Wait, 16 km in 4 minutes: 4 km/min. 21 km in 7 minutes: 3 km/min. 27 km in 9 minutes: 3 km/min. So the speed is not constant. So the first option is correct.

Part (a) - Predicted Time for 30 Kilometers

Wait, but if the speed is not constant, how do we predict? But maybe I made a mistake in the speed calculation. Wait, maybe the table is 16, 24, 27? No, the user provided 21. Wait, maybe the problem has a typo, but assuming that the second and third data points have a speed of 3 km/min, and the first is 4, but maybe it's a mistake. Alternatively, maybe I miscalculated. Wait, 16 divided by 4 is 4, 21 divided by 7 is 3, 27 divided by 9 is 3. So the speed is 4, 3, 3. But that's inconsistent. Alternatively, maybe the time for 16 km is 4 minutes, 21 km is 5.25 minutes? No, the table says 7. Wait, maybe the problem is correct, and we need to see if there's a pattern. Wait, 16 km in 4 min: 4 km/min. 21 km in 7 min: 3 km/min. 27 km in 9 min: 3 km/min. So maybe the first data point is an error, or maybe I misread. Wait, maybe the distance is 12, 21, 27? Then 12/4=3, 21/7=3, 27/9=3. That would make sense. Maybe the table has a typo, and 16 is 12. But assuming the table is correct as given, maybe the intended speed is 3 km/min. Let's check: 16/4=4, 21/7=3, 27/9=3. So maybe the first data point is an outlier, and the rest have speed 3. So we'll use 3 km/min for prediction. Then time for 30 km is \( \frac{30}{3} = 10 \) minutes.

Final Answers

• Correct description: The train does not always go the same distance each minute.
• Predicted time: 10 minutes (assuming speed of 3 km/min, ignoring the first data point's speed as an outlier, or maybe the table has a typo).

But wait, let's re-express:

For the first part, calculating speed:

1. \( \frac{16}{4} = 4 \) km/min
2. \( \frac{21}{7} = 3 \) km/min
3. \( \frac{27}{9} = 3 \) km/min

Since the speeds are not the same (4, 3, 3), the train does not always go the same distance each minute. So the first option is correct.

For the predicted time, if we consider the last two data points (which have the same speed of 3 km/min), we can use that speed. So speed \( v = 3 \) km/min. Then time \( t = \frac{\text{distance}}{v} = \frac{30}{3} = 10 \) minutes.

So:

(a) The correct description is "The train does not always go the same distance each minute."

Predicted time to travel 30 kilometers: 10 minutes.