Question

Из пункта А в пункт Б отправился велосипедист Вася, а через 2 минуты ему навстречу из Б в А выехал велосипедист Петя. От места встречи на дороге Вася добрался до пункта Б за 11 минут, а Петя до пункта А за 9 минут. Сколько минут был в пути каждый из них?

Answer 1

Ответ:

Вася ехал 18 минут, а Петя 14 минут

Пошаговое объяснение:

 Пусть Х -время Васи, У время Пети.

Пусть S - путь

(S-2*S/у)/((S/х)+(S/у))-время встречи с момента выезда Пети

Преобразуя:

Т=(ху-2х)/(х+у) время встречи с момента выезда Пети

Т+2+11=х

Т+9=у

х-у=4

х=4+у

Подставляем в (ху-2х)/(х+у)+9=у

Преобразуя, получим  (у+4)*(у-2)=2*(у+2)*(у-9)

Получим  y^2-16y-28=0

Два корня у=14 и у=2. Имеет смысл у=14

х=18

Answer 2

Problem Analysis

We are given that cyclist Vasya traveled from point A to point B on a bicycle, and after 2 minutes, cyclist Petya traveled from point B to point A. Vasya reached point B in 11 minutes, and Petya reached point A in 9 minutes. We need to determine how many minutes each of them was on the road.

Solution

Let's assume that the distance between point A and point B is d kilometers.

Since Vasya traveled from A to B in 11 minutes, we can calculate his speed as d/11 kilometers per minute.

Similarly, since Petya traveled from B to A in 9 minutes, we can calculate his speed as d/9 kilometers per minute.

Since they traveled towards each other, their combined speed is the sum of their individual speeds:

Vasya's speed + Petya's speed = d/11 + d/9 = (9d + 11d)/(9 * 11) = 20d/99 kilometers per minute.

We know that they met after 2 minutes, so the total distance they covered in those 2 minutes is:

2 * (20d/99) = 40d/99 kilometers.

Since the total distance between A and B is d kilometers, we can set up the following equation:

d - (40d/99) = d(1 - 40/99) = d(59/99) = d * 59/99.

Therefore, Vasya traveled d * 59/99 kilometers in 11 minutes, and Petya traveled d * 59/99 kilometers in 9 minutes.

Answer

Vasya was on the road for 11 minutes, and Petya was on the road for 9 minutes.

Note: The above solution assumes that the speeds of Vasya and Petya remain constant throughout their journey.