Question

За 4 ч поезд преодолел расстояние в 360 км. Во сколько раз большее расстояние преодолеет этот поезд за 12 ч если будет двигатся с той же средней скоростью? Рассмотри и объясни каждый из двух выриантов решения этой задачи

Answer 1

1) 360:4=90(км/ч)
2) 90*12=1080(км)

Answer 2

Problem Analysis

We are given that a train traveled a distance of 360 km in 4 hours. We need to determine how much greater distance the train will cover in 12 hours if it continues to travel at the same average speed.

Solution 1: Using Proportions

We can solve this problem using proportions. The ratio of distance to time is constant for a given speed. Therefore, if the train traveled 360 km in 4 hours, the ratio of distance to time is 360/4 = 90 km/h.

To find the distance the train will cover in 12 hours, we can set up the proportion:

360 km / 4 hours = x km / 12 hours

Solving this proportion will give us the distance the train will cover in 12 hours.

Solution 2: Using Speed and Time Relationship

Alternatively, we can use the relationship between speed, distance, and time to solve this problem. The formula to calculate distance is:

Distance = Speed × Time

Given that the train traveled 360 km in 4 hours, we can calculate the average speed of the train:

Speed = Distance / Time = 360 km / 4 hours = 90 km/h

Now, we can use this average speed to calculate the distance the train will cover in 12 hours:

Distance = Speed × Time = 90 km/h × 12 hours

Solving this equation will give us the distance the train will cover in 12 hours.

Solution Comparison

Both solutions will give us the same result. Let's calculate the distance using both methods to verify this.

Solution

Using Solution 1 (Proportions): To find the distance the train will cover in 12 hours, we can set up the proportion:

360 km / 4 hours = x km / 12 hours

Cross-multiplying, we get:

360 km × 12 hours = 4 hours × x km

Simplifying, we have:

4320 km = 4x km

Dividing both sides by 4, we find:

x km = 1080 km

Therefore, the train will cover a distance of 1080 km in 12 hours if it continues to travel at the same average speed.

Using Solution 2 (Speed and Time Relationship): Given that the average speed of the train is 90 km/h, we can calculate the distance it will cover in 12 hours:

Distance = Speed × Time = 90 km/h × 12 hours = 1080 km

Therefore, the train will cover a distance of 1080 km in 12 hours if it continues to travel at the same average speed.

Conclusion

Both solutions yield the same result. The train will cover a distance of 1080 km in 12 hours if it continues to travel at the same average speed of 90 km/h.

Please let me know if anything is unclear or if you have any further questions!