Question

Из пунктов А и В в 10 часов утра выехали в противоположных направлениях, удаляясь друг от друга, два велосипедиста. Через 2 часа расстояние между ними увеличилось на 64 км. В этот момент они развернулись и не останавливаясь, и не меняя скорости, поехали в обратную сторону, навстречу друг другу. До разворота один из велосипедистов проехал 36 км. Найди расстояние между пунктами А и В, если известно, что встреча произошла в 6 часов вечера.

Answer 1

1) 36 : 2 = 18 км/ч скорость одного велосипедиста
2) 64 - 36 = 28 км проехал до разворота другой велосипедист
3) 28 : 2 = 14 км/ч скорость второго велосипедиста
4) 10 + 2 = 12 часов было когда они разворачивались
5) 18 + 14 = 32 км/ч скорость сближения
6) 18 - 12 = 6 часов ехали до встречи
7) 32 * 6 = 192 км проехали до встречи
8) 192 - 64 = 128 км расстояние между А и В

Answer 2

Problem Analysis

We have two cyclists who start at points A and B and move away from each other in opposite directions. After 2 hours, the distance between them increases by 64 km. They then turn around without stopping or changing their speed and start moving towards each other. At the moment they turn around, one of the cyclists has traveled 36 km. We need to find the distance between points A and B, given that they meet at 6 PM.

Solution

Let's break down the problem step by step:

1. The distance between the two cyclists increased by 64 km in 2 hours. This means that their combined speed is 64 km / 2 hours = 32 km/h.

2. One of the cyclists traveled 36 km before turning around. Since the combined speed is 32 km/h, it took them 36 km / 32 km/h = 1.125 hours to reach the turning point.

3. The total time from the start until they meet is 6 PM - 10 AM = 8 hours.

4. The time it took for the first cyclist to reach the turning point is 1.125 hours. Therefore, the time remaining until they meet is 8 hours - 1.125 hours = 6.875 hours.

5. Since they are moving towards each other, their combined speed is still 32 km/h. Therefore, the distance they will cover in 6.875 hours is 32 km/h * 6.875 hours = 220 km.

6. Since the distance between the two cyclists at the start was 0 km, the total distance between points A and B is 220 km + 64 km = 284 km.

Therefore, the distance between points A and B is 284 km.

Please note that the solution assumes a constant speed throughout the entire journey and does not take into account any other factors that may affect the actual distance traveled.