Question

Из Уральска в Актобе на встречу друг другу вышли два поезда.Они встретились через 4 целых одна чётвёртая.1 из них проехал проехал 382целых одна вторая а другой 300целых девять десятых на сколько километров приблизились эти 2 поезда через 1 час.если сможете пожалуйста 2 способа

Answer 1

(382,5+300,9)/4,25=160,8 км

Answer 2

Problem Analysis

We have two trains traveling towards each other from Uralsk to Aktobe. They meet after 4 and 1/4 hours. One train travels 382 and 1/2 kilometers, while the other travels 300 and 9/10 kilometers. We need to determine how close the trains are after 1 hour.

Solution

To solve this problem, we can use the formula: Distance = Speed × Time.

Let's calculate the speeds of the two trains first.

Train 1: - Distance traveled: 382 and 1/2 kilometers - Time taken: 4 and 1/4 hours - Speed = Distance / Time

Train 2: - Distance traveled: 300 and 9/10 kilometers - Time taken: 4 and 1/4 hours - Speed = Distance / Time

Now that we have the speeds of both trains, we can calculate how close they are after 1 hour.

Calculation

Let's calculate the speeds of the two trains first.

Train 1: - Distance traveled: 382 and 1/2 kilometers - Time taken: 4 and 1/4 hours - Speed = Distance / Time = (382.5 km) / (4.25 hours) = 90 km/h

Train 2: - Distance traveled: 300 and 9/10 kilometers - Time taken: 4 and 1/4 hours - Speed = Distance / Time = (300.9 km) / (4.25 hours) = 70.8 km/h

Now that we have the speeds of both trains, we can calculate how close they are after 1 hour.

Train 1: - Distance traveled after 1 hour = Speed × Time = (90 km/h) × (1 hour) = 90 km

Train 2: - Distance traveled after 1 hour = Speed × Time = (70.8 km/h) × (1 hour) = 70.8 km

Therefore, the two trains will be approximately 90 km apart after 1 hour.

Alternative Method 1: Relative Speed

Another way to solve this problem is by considering the relative speed of the two trains. The relative speed is the sum of the speeds of the two trains.

Relative speed = Speed of Train 1 + Speed of Train 2

Relative speed = 90 km/h + 70.8 km/h = 160.8 km/h

Since the two trains are moving towards each other, the distance between them will decrease at a rate equal to the relative speed.

Distance decreased after 1 hour = Relative speed × Time = (160.8 km/h) × (1 hour) = 160.8 km

Therefore, the two trains will be approximately 160.8 km closer to each other after 1 hour.

Alternative Method 2: Proportional Division

We can also solve this problem using proportional division.

The total distance between the two trains is the sum of the distances traveled by each train.

Total distance = Distance traveled by Train 1 + Distance traveled by Train 2

Total distance = (382 and 1/2 km) + (300 and 9/10 km) = (382.5 km) + (300.9 km) = 683.4 km

Since the two trains meet after 4 and 1/4 hours, we can find the distance between them after 1 hour by dividing the total distance by the total time.

Distance between the two trains after 1 hour = Total distance / Total time = (683.4 km) / (4.25 hours) = 160.8 km

Therefore, the two trains will be approximately 160.8 km closer to each other after 1 hour.

Please let me know if you need any further assistance!