Question

Мотоциклист и велосипедист одновременно отправились из пункта А в пункт В расстояние между которыми 90 км. скорость велосипедиста 10 км/ч, скорость мотоциклиста 45 км/ч. Ровно на середине дороги мотоцикл заглох, и дальше мотоциклист шёл со скоростью 3 км/ч. Через сколько часов после начала движения велосипедист догонит моточиклиста.

Answer 1

45:45= 1 час проехал мотоциклист до того как заглох
10*1= 10 км проехал велосипедист за первый час
45-10= 35 км расстояние между ними через час движения
35:(10-3)= 5 часов  
Ответ: через пять часов велосипедист догонит мотоциклиста

Answer 2

Calculating When the Cyclist Overtakes the Motorcyclist

To calculate when the cyclist overtakes the motorcyclist, we can use the concept of relative speed. The relative speed of the cyclist with respect to the motorcyclist is the difference between their speeds. We can then use this relative speed to calculate the time it takes for the cyclist to catch up to the motorcyclist.

Given: - Distance between points A and B = 90 km - Speed of the cyclist = 10 km/h - Speed of the motorcyclist = 45 km/h (initially), 3 km/h (after the motorcycle breaks down)

Calculating the Time Taken

First, we need to find the time it takes for the motorcyclist to break down. We can use the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

The time taken for the motorcyclist to break down is: \[ \text{Time} = \frac{90 \text{ km}}{45 \text{ km/h}} = 2 \text{ hours} \]

After the breakdown, the motorcyclist walks at 3 km/h. Now, we can calculate the time it takes for the cyclist to catch up to the motorcyclist using the relative speed formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

The relative speed of the cyclist with respect to the motorcyclist is: \[ \text{Relative Speed} = 45 \text{ km/h} - 10 \text{ km/h} = 35 \text{ km/h} \]

Substituting the values, we get: \[ \text{Time} = \frac{90 \text{ km}}{35 \text{ km/h}} \approx 2.57 \text{ hours} \]

So, the cyclist will catch up to the motorcyclist approximately 2.57 hours after the start of their journey.

Final Answer

The cyclist will catch up to the motorcyclist approximately 2.57 hours after the start of their journey.