Question

Два друга Олег и Антон выходят одновременно из пунктов A и B навстречу друг другу и встречаются через 18 минут. Олег проходит расстояние AB за 30 минут. За сколько минут проходит расстояние AB другой друг, Антон?

Answer 1

Х-скорость Олега
у-скорость Антона
18*(х+у)-расстояние АВ
18(х+у)/х=30
18х+18у=30х=18у=12х
х=18у/12=1,5у⇒скорость Олега в 1,5 раза больше,значит время Антона в 1,5раза больше
30*1,5=45 минут проходит Антон

Answer 2

Problem Analysis

We are given that two friends, Oleg and Anton, start walking towards each other from points A and B simultaneously. They meet after 18 minutes, and we are told that Oleg covers the distance AB in 30 minutes. We need to determine how long it takes Anton to cover the distance AB.

Solution

Let's assume that Anton takes x minutes to cover the distance AB. Since Oleg covers the distance AB in 30 minutes, we can set up the following equation:

Oleg's speed = Distance / Time = AB / 30

Anton's speed = Distance / Time = AB / x

Since they meet after 18 minutes, the total distance covered by Oleg and Anton combined is AB. Therefore, we can set up the following equation:

Oleg's distance + Anton's distance = AB

(Oleg's speed) * (Oleg's time) + (Anton's speed) * (Anton's time) = AB

(AB / 30) * 30 + (AB / x) * x = AB

AB + AB = AB

2AB = AB

AB = 18

Therefore, the distance AB is 18 units.

Now, we can substitute this value back into the equation to find Anton's time:

(AB / x) * x = AB

(18 / x) * x = 18

x = 18

Therefore, Anton takes 18 minutes to cover the distance AB.

Answer

Anton takes 18 minutes to cover the distance AB.