Question

Из пункта А в пункт В со скоростью 18км/ч выехал велосипедист, а через 1 час навстречу ему из пункта В со скоростью 65км/ч выехал мотоциклист. На каком расстоянии от пункта А произошла встреча велосипедиста и мотоциклиста, если известно, что расстояние между пунктами А и В равно 350км?

Answer 1

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Answer 2

Problem Analysis

We are given that a cyclist starts from point A and travels towards point B at a speed of 18 km/h. After 1 hour, a motorcyclist starts from point B and travels towards point A at a speed of 65 km/h. We need to find the distance from point A where the cyclist and the motorcyclist meet, given that the distance between points A and B is 350 km.

Solution

Let's assume that the distance from point A to the meeting point is x km. Since the cyclist travels for 1 hour at a speed of 18 km/h, the distance covered by the cyclist in 1 hour is 18 km. Therefore, the remaining distance from the meeting point to point B is (350 - x) km.

Similarly, the motorcyclist travels for 1 hour at a speed of 65 km/h, covering a distance of 65 km. Therefore, the remaining distance from the meeting point to point A is (x - 65) km.

Since the total distance from the meeting point to point B is equal to the total distance from the meeting point to point A, we can set up the following equation:

(350 - x) km = (x - 65) km

Simplifying the equation, we get:

350 - x = x - 65

Solving for x, we find:

2x = 415

x = 207.5 km

Therefore, the meeting point is located 207.5 km from point A.

Answer

The meeting point between the cyclist and the motorcyclist is located 207.5 km from point A.