Question

Найди разные способы решения задачи Два поезда вышли одновременно с одной станции в одном направлении. Скорость одного поезда 75 км/ч, а другого 82 км/ч. На каком расстоянии друг от друга они будут через 3 часа.

Answer 1

1. (82-75)*3=21 2. 82*3-75*3=21

Answer 2

Problem Statement

Два поезда вышли одновременно с одной станции в одном направлении. Скорость одного поезда составляет 75 км/ч, а другого - 82 км/ч. На каком расстоянии друг от друга они будут через 3 часа?

Solution 1: Using the formula Distance = Speed * Time

To find the distance between the two trains after 3 hours, we can use the formula Distance = Speed * Time. We'll calculate the distance traveled by each train separately and then find the difference between their distances.

Train 1: - Speed: 75 km/h - Time: 3 hours - Distance traveled by Train 1 = Speed * Time = 75 km/h * 3 hours = 225 km

Train 2: - Speed: 82 km/h - Time: 3 hours - Distance traveled by Train 2 = Speed * Time = 82 km/h * 3 hours = 246 km

The distance between the two trains after 3 hours is the difference between their distances: Distance = Distance of Train 2 - Distance of Train 1 = 246 km - 225 km = 21 km

Therefore, the two trains will be 21 km apart after 3 hours.

Solution 2: Using relative speed

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

Relative speed = Speed of Train 2 - Speed of Train 1 = 82 km/h - 75 km/h = 7 km/h

To find the distance between the two trains after 3 hours, we can use the formula Distance = Speed * Time. In this case, the speed is the relative speed.

Distance = Relative speed * Time = 7 km/h * 3 hours = 21 km

Therefore, the two trains will be 21 km apart after 3 hours.

Solution 3: Using the Pythagorean theorem

We can also solve this problem using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, we can consider the distance traveled by each train as one side of a right triangle, and the distance between the two trains as the hypotenuse.

Using the formula c^2 = a^2 + b^2, where c is the hypotenuse and a and b are the other two sides, we can calculate the distance between the two trains.

Train 1: - Speed: 75 km/h - Time: 3 hours - Distance traveled by Train 1 = Speed * Time = 75 km/h * 3 hours = 225 km

Train 2: - Speed: 82 km/h - Time: 3 hours - Distance traveled by Train 2 = Speed * Time = 82 km/h * 3 hours = 246 km

Using the Pythagorean theorem: c^2 = a^2 + b^2 Distance^2 = (Distance of Train 1)^2 + (Distance of Train 2)^2 Distance^2 = 225 km^2 + 246 km^2 Distance^2 = 50625 km^2 + 60516 km^2 Distance^2 = 111141 km^2

Taking the square root of both sides: Distance = sqrt(111141) km ≈ 333.48 km

Therefore, the two trains will be approximately 333.48 km apart after 3 hours.

Conclusion

There are multiple ways to solve the problem of finding the distance between two trains that leave a station simultaneously in the same direction. Using the given speeds and the time, we can calculate the distance traveled by each train and find the difference between their distances. Alternatively, we can consider the relative speed of the two trains and calculate the distance using the formula Distance = Speed * Time. Another approach is to use the Pythagorean theorem to calculate the distance as the hypotenuse of a right triangle formed by the distances traveled by each train. In this case, the distances are squared and then added together before taking the square root.