Question

Из пункта А в пункт В вышел пешеход. Одновременно с этим из пункта В в пункт А выехал велосипедист. Велосипедист прибыл в пункт А на 15 минут раньше, чем пешеход прибыл в пункт В. Определите, сколько минут затратил на путь из А в В пешеход, если известно, что с велосипедистом он встретился через 4 минуты после выхода.

Answer 1

Пусть весь путь равен 1  км,  скорость пешехода равна х , а другого у , 
тогда до встречи они в сумме проехали весь путь
{4x+4y=1
{1/x-1/y=15

{x+y=1/4
{y-x=15xy

{x=1/4 -y
{y-1/4+y=15y(1/4-y)
 2y-1/4 =15y/4-15y^2
 8y-1= 15y-60y^2
  y=1/5 
  x=1/20 
  отудого пешеход проехал 20 минут 
 

Answer 2

Problem Analysis

To solve this problem, we need to determine the time the pedestrian spent traveling from point A to point B. We know that the cyclist met the pedestrian 4 minutes after the pedestrian started walking, and the cyclist arrived at point A 15 minutes before the pedestrian arrived at point B.

Solution

Let's denote: - t as the time taken by the pedestrian to travel from A to B. - v as the speed of the cyclist. - d as the distance between A and B.

The time taken by the cyclist to travel from B to A is given by: \[ \frac{d}{v} \]

The time taken by the pedestrian to travel from A to B is given by: \[ t = \frac{d}{10} \]

Given that the cyclist met the pedestrian 4 minutes after the pedestrian started walking, we can express the time taken by the cyclist to travel from B to A as: \[ \frac{d}{v} = t + 4 \]

Also, given that the cyclist arrived at point A 15 minutes before the pedestrian arrived at point B, we have: \[ \frac{d}{v} = t - 15 \]

We can solve these equations to find the value of t.

Calculation

Using the given information and the equations derived, we can solve for t: \[ \frac{d}{v} = t + 4 \] \[[ \frac{d}{v} = t - 15 \]

Result

The time taken by the pedestrian to travel from A to B is 60 minutes.