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 (km)
12
24
32
Time (in minutes)
3
6
8
O The train does not always go the same distance each minute.
O The train appears to go the same distance each minute.
Predicted distance traveled in 9 minutes: km

Answer 1

To predict the distance traveled in 9 minutes, we can use the data provided in the table and observe the pattern between distance and time.

From the table, we can see that the train covers 12 km in 3 minutes, which means it travels at a rate of 4 km per minute (12 km / 3 minutes = 4 km/minute). This rate appears consistent as the train takes the same amount of time to cover each additional distance:

24 km in 6 minutes (24 km / 6 minutes = 4 km/minute)

32 km in 8 minutes (32 km / 8 minutes = 4 km/minute)

Since the rate of travel is constant at 4 km per minute, we can predict that the train will cover 4 km in 1 minute. Therefore, in 9 minutes, the train will travel:

Distance = Rate × Time

Distance = 4 km/minute × 9 minutes

Distance = 36 km

The predicted distance traveled by the train in 9 minutes is 36 km.

Answer 2

Predicted distance traveled in 9 minutes: 36 km

Explanation:

The relation between distance and speed is that they are directly proportional to each other. This means that if the speed of an object increases, the distance it travels will also increase.

For the question:

Given:

• Distance traveled in 3 minutes = 12 km
• Distance traveled in 6 minutes = 24 km
• Distance traveled in 8 minutes = 32 km

Assumption:

The average speed of the train between 3 and 6 minutes is 4 km/minute

The average speed between 6 and 8 minutes is also 4 km/minute.

Prediction:

The predicted distance traveled in 9 minutes is 36 kilometers.

The train maintains a constant speed.

Calculation:

`\boxed{\textsf{Average speed} =\frac{\textsf{ Distance traveled} }{\textsf{Time taken}}}`

`\sf \textsf{Average speed }= (12)/(3) =(24)/(6)=(32)/(8)=4 km/minute`

`\boxed{\textsf{Distance traveled = Speed *Time}}`

Distance traveled in 9 minutes = 4 km/minute*9 minutes

Distance traveled in 9 minutes = 36 km

Conclusion:

The predicted distance traveled by the train in 9 minutes is 36 kilometers. This is based on the assumption that the train maintains a constant speed of 4 km/minute.

The actual distance traveled by the train could be different, depending on the factors that affect the train's speed.