Answer:
A. To predict the distance traveled by the train in 9 minutes, we can analyze the given data points. The table shows the distance and the corresponding time it takes for the train to travel.
From the given data:
- Distance (km): 8, 12, 32
- Time (minutes): 2, 3, 8
To determine a pattern, we can calculate the distance traveled per minute for each time interval given:
- Between the first two points, the train travels a difference of 4 km in 1 minute (12 km - 8 km). So the train is traveling at a rate of 4 km/minute.
- Between the second and third points, the train travels a difference of 20 km in 5 minutes (32 km - 12 km). So the train is traveling at a rate of 4 km/minute.
- Based on this pattern, we can assume that the train maintains a constant speed of 4 km/minute.
Using this assumption, we can calculate the predicted distance traveled in 9 minutes:
4 km/minute × 9 minutes = 36 km
Therefore, the predicted distance traveled by the train in 9 minutes is 36 km.
B. To predict the number in the group for a cost of $50, we can analyze the data provided in the table. Let's first observe the pattern for the cost per person:
For a group of 3 people, the cost is $18. Hence, the cost per person is $18/3 = $6.
For a group of 7 people, the cost is $35. Therefore, the cost per person is $35/7 = $5.
For a group of 9 people, the cost is $45. Thus, the cost per person is $45/9 = $5.
From the given data, we can see that the cost per person appears to be consistently $5, except for the group of 3 people where it is $6.
To predict the number in the group for a cost of $50, we need to find out how many times $5 fits into $50.
$50 ÷ $5 = 10
Thus, based on the pattern observed, we can predict that the number in the group for a cost of $50 would be 10.