Question

Из поселка на станцию,расстояние между которыми 32 км,выехал велосипедист.Через 0,5 ч навстречу ему со станции выехал мотоциклист и встретил велосипедиста через 0,5 ч после своего выезда Известно,что скорость мотоциклиста на 28 км\ч больше скорости велосипедиста.Найдите скорость каждого из них

Answer 1

Пусть скорость велосипедиста  будет х км/ч
 Тогда скорость мотоциклиста х+28 км/ч
Велосипедист был в пути 0,5ч+0,5ч=1час до встречи.
х*1час+(х+28)*0,5час= 32 км
х=12 км./час скорость велосипедиста
12+28=40 км/час скорость мотоциклиста

Answer 2

Problem Analysis

A cyclist starts from a village and travels towards a train station, which is 32 km away. After 0.5 hours, a motorcyclist starts from the train station and meets the cyclist 0.5 hours after their own departure. It is known that the motorcyclist's speed is 28 km/h faster than the cyclist's speed. We need to find the speed of each of them.

Solution

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

To solve this problem, we can use the formula: distance = speed × time.

The cyclist travels for 0.5 hours before meeting the motorcyclist. Therefore, the distance traveled by the cyclist is 0.5 × x km.

The motorcyclist travels for 0.5 hours before meeting the cyclist. Therefore, the distance traveled by the motorcyclist is 0.5 × (x + 28) km.

Since the total distance between the village and the train station is 32 km, we can set up the following equation:

0.5 × x + 0.5 × (x + 28) = 32

Now, let's solve this equation to find the value of x.

Calculation

0.5x + 0.5(x + 28) = 32

0.5x + 0.5x + 14 = 32

1x + 14 = 32

1x = 32 - 14

1x = 18

x = 18

Answer

The speed of the cyclist is 18 km/h and the speed of the motorcyclist is 18 + 28 = 46 km/h.

Please note that the above solution assumes a linear relationship between time and distance traveled. It also assumes that the speeds of the cyclist and motorcyclist remain constant throughout their journey.