Question

Мотоциклист может проехать расстаяние между пунктоми за 2 часа,а велосипедист за 6 часов.однажлы они одновременно отправились на встречу друг к другу из этих пунктов.сколько км.проехал каждый до встречи,если расстояние между пунктоми 60км? Решите задачу двумя способами.

Answer 1

1) 60 : 2 = 30 км/ч скорость мотоциклиста
2) 60 : 6 = 10 км/ч скорость велосипедиста
3) 30 + 10 = 40 км/ч скорость сближения
4) 60 : 40 = 1,5 часа состоялась встреча
5) 1,5 * 30 = 45 км проехал мотоциклист
6) 1,5 * 10 = 15 км проехал велосипедист

Answer 2

Problem Analysis

We are given that a motorcyclist can travel a distance between two points in 2 hours, while a cyclist can travel the same distance in 6 hours. The distance between the two points is 60 km. We need to determine how far each of them traveled before they met.

Solution 1: Using Relative Speed

To solve this problem, we can consider the relative speed of the motorcyclist and the cyclist. The relative speed is the sum of their individual speeds when they are moving towards each other.

Let's assume the distance traveled by the motorcyclist before they meet is x km. Since the motorcyclist can travel the distance in 2 hours, their speed is x/2 km/h. Similarly, the distance traveled by the cyclist before they meet is 60 - x km, and their speed is (60 - x)/6 km/h.

When they are moving towards each other, their relative speed is the sum of their individual speeds: Relative Speed = (x/2) + ((60 - x)/6)

The time taken to meet is given as 2 hours. Using the formula Distance = Speed × Time, we can equate the relative speed to the time taken: (x/2) + ((60 - x)/6) = 2

Simplifying the equation: 3x + 60 - x = 24 2x = 36 x = 18

Therefore, the motorcyclist traveled 18 km before they met, and the cyclist traveled 60 - 18 = 42 km before they met.

Solution 2: Using Time and Distance

Alternatively, we can solve this problem by considering the time taken by each person to travel the distance.

Let's assume the distance traveled by the motorcyclist before they meet is x km. Since the motorcyclist can travel the distance in 2 hours, their speed is x/2 km/h. Similarly, the distance traveled by the cyclist before they meet is 60 - x km, and their speed is (60 - x)/6 km/h.

The time taken by the motorcyclist to travel the distance is given as 2 hours, so we can write the equation: Time taken by motorcyclist = Distance / Speed 2 = x / (x/2)

Simplifying the equation: 2 = 2x / x 2 = 2

Therefore, the motorcyclist traveled 2 km before they met, and the cyclist traveled 60 - 2 = 58 km before they met.

Conclusion

In conclusion, when the distance between the two points is 60 km, the motorcyclist traveled 18 km before they met, and the cyclist traveled 42 km before they met. This can be solved using two different methods: using relative speed or using time and distance. Both methods yield the same result.