Question

Из пункта А в пункт В,расстояние между которыми 26 км ,выехал велосипедист.Одновременно с ним из В в А выехал мотоциклист со скоростью,на 28 км\ч большей скорости велосипедиста.Они встретились через 0.5 ч. Найдите скорость мотоциклистаю На каком расстоянии от пункта А произошла встреча?

Answer 1

х - скорость велосипедиста

х+28 - скорость мотоциклиста

 

х/2 - расстояние, которое проехал до встречи велосипедист

 

(х+28)/2 - расстояние, которое проехал до встречи мотоциклист

 

х/2+(х+28)/2=26

х+х+28=52

2х=24

х=24:2=12

 

х/2=12:2=6 (км) - расстояние, которое проехал до встречи велосипедист (то есть на таком расстоянии от пункта А произошла встреча)

 

 

Answer 2

Problem Analysis

We are given that a cyclist and a motorcyclist start from points A and B, respectively, which are 26 km apart. The motorcyclist travels at a speed 28 km/h faster than the cyclist. They meet after 0.5 hours. We need to find the speed of the motorcyclist and the distance from point A where they meet.

Solution

Let's assume the speed of the cyclist is x km/h. Since the motorcyclist is traveling 28 km/h faster, their speed is x + 28 km/h.

We know that the time taken by both the cyclist and the motorcyclist to meet is 0.5 hours.

To find the distance from point A where they meet, we can use the formula:

Distance = Speed × Time

Let's calculate the distance from point A where they meet:

Distance = (Speed of the cyclist) × (Time taken by both to meet)

Distance = x × 0.5

The distance from point A where they meet is also the distance traveled by the cyclist. So, the distance traveled by the cyclist is 0.5x km.

Since the total distance between points A and B is 26 km, we can write the equation:

Distance traveled by the cyclist + Distance traveled by the motorcyclist = Total distance

0.5x + (0.5x + 28) = 26

Simplifying the equation:

x + x + 28 = 52

2x = 24

x = 12

Therefore, the speed of the cyclist is 12 km/h.

To find the speed of the motorcyclist, we can substitute the value of x into the equation:

Speed of the motorcyclist = Speed of the cyclist + 28

Speed of the motorcyclist = 12 + 28

Speed of the motorcyclist = 40 km/h

So, the speed of the motorcyclist is 40 km/h.

To find the distance from point A where they meet, we can substitute the value of x into the equation:

Distance from point A = Speed of the cyclist × Time taken by both to meet

Distance from point A = 12 × 0.5

Distance from point A = 6 km

Therefore, the motorcyclist and the cyclist meet at a distance of 6 km from point A.

Answer

The speed of the motorcyclist is 40 km/h. The meeting point is 6 km from point A.