Question

Из поселка на станцию удаленную от него на расстояние 27 км, отправились одновременно пешеход и велосипедист, причем скорость пешехода была на 10 км/ч меньше скорости велосипедиста. Прибыв на станцию, велосипедист сразу повернул обратно и встретил пешехода через 2 часа 24мин. после его выхода из поселка. На каком расстоянии от поселка произошла встреча?

Answer 1

Пусть x будет скорость пешехода, тогда скорость велосепидиста будет x+10'

 

2,4x=27-((x+10)*2,4-27)

2,4x=27-(2,4x+24-27)

2,4x=27-2,4x-24+27

4,8x =30

x=6,25 (Это мы нашли V пешехода)

 

А расстояние будет равно -  6,25*2,4=15. Они встретились на 15 км

 

Удачи!

Answer 2

Problem Analysis

We are given that a pedestrian and a cyclist start simultaneously from a village and travel to a station located 27 km away from the village. The pedestrian's speed is 10 km/h less than the cyclist's speed. After reaching the station, the cyclist immediately turns back and meets the pedestrian 2 hours and 24 minutes after the pedestrian leaves the village. We need to determine the distance from the village where they meet.

Solution

Let's denote the speed of the cyclist as v km/h. According to the problem, the speed of the pedestrian is 10 km/h less than the cyclist's speed, so the pedestrian's speed is v - 10 km/h.

We can calculate the time it takes for the pedestrian to reach the station using the formula:

time = distance / speed

The distance from the village to the station is 27 km, and the speed of the pedestrian is v - 10 km/h. Therefore, the time taken by the pedestrian to reach the station is:

time_pedestrian = 27 / (v - 10)

After reaching the station, the cyclist immediately turns back and meets the pedestrian 2 hours and 24 minutes (or 2.4 hours) after the pedestrian leaves the village. This means that the cyclist travels for a total of 2.4 hours + time_pedestrian.

To find the distance from the village where they meet, we need to calculate the distance traveled by the cyclist. We can use the formula:

distance = speed * time

The speed of the cyclist is v km/h, and the time traveled by the cyclist is 2.4 hours + time_pedestrian. Therefore, the distance traveled by the cyclist is:

distance_cyclist = v * (2.4 + time_pedestrian)

Since the cyclist travels back to the village, the total distance traveled by the cyclist is twice the distance from the village to the meeting point. Therefore, we can write:

2 * distance_from_village_to_meeting_point = distance_cyclist

Substituting the values, we get:

2 * distance_from_village_to_meeting_point = v * (2.4 + time_pedestrian)

Now, we can solve this equation to find the distance from the village where the meeting occurs.

Let's calculate the values step by step.

1. Calculate the time taken by the pedestrian to reach the station: time_pedestrian = 27 / (v - 10)

2. Calculate the distance traveled by the cyclist: distance_cyclist = v * (2.4 + time_pedestrian)

3. Calculate the distance from the village to the meeting point: distance_from_village_to_meeting_point = distance_cyclist / 2

4. Substitute the values and solve the equation: 2 * distance_from_village_to_meeting_point = v * (2.4 + time_pedestrian)

Let's calculate the values using the given information.