Question

Мама гуляет с коляской вокруг озера и полностью обходит озеро за 12 минут.Ваня по той же дорожке в ту же сторону ездит на самокате и встречает маму каждые 12 минут.через какие промежутки времени Ваня будет встречать маму,если он будет ездить с той же скоростью,но в обратном направлении? Пожалуйста сделайте завтра олимпиада по алгебре , прошу!!!

Answer 1

Пусть х м - длина дорожки вокруг озера, тогда скорость мамы равна $\frac{x}{12}$ м/мин, а скорость Вани - $\frac{x}{6}$ м/мин, так как скорость Вани в 2 раза больше скорости мамы

Мама и Ваня едут навстречу друг другу, значит скорость сближения равна $\frac{3x}{12} = \frac{x}{4}$ м/мин отсюда вместе расстояние они преодолеют за 4 мин

Ответ: будут встречаться раз в 4 минуты

Answer 2

Problem Analysis

To solve this problem, we need to find the intervals at which Vanya will meet his mother if he travels in the opposite direction around the lake at the same speed.

Solution

Let's start by analyzing the situation. We know that Vanya meets his mother every 12 minutes when he travels in the same direction. Now, we need to find out how often he will meet his mother when he travels in the opposite direction.

When Vanya and his mother are both traveling in the same direction, they cover the entire circumference of the lake in 12 minutes. If Vanya travels in the opposite direction, he will effectively be reducing the relative speed between him and his mother, which will result in more frequent meetings.

To find the intervals at which Vanya will meet his mother when traveling in the opposite direction, we can use the concept of relative speed.

Relative Speed

When two objects are moving in the same direction, their relative speed is the difference between their individual speeds. When they are moving in opposite directions, their relative speed is the sum of their individual speeds.

Let's denote: - Vanya's speed as V (in units of distance per time) - Mother's speed as M (in units of distance per time)

When Vanya and his mother are moving in the same direction, their relative speed is M - V. When they are moving in opposite directions, their relative speed is M + V.

Calculating the Intervals

To calculate the intervals at which Vanya will meet his mother when traveling in the opposite direction, we can use the formula: Time = Distance / Relative Speed

Since the distance around the lake remains the same, we can use the same distance for both scenarios.

Let's calculate the intervals at which Vanya will meet his mother when traveling in the opposite direction.

Results

The intervals at which Vanya will meet his mother when traveling in the opposite direction can be calculated using the formula: Time = Distance / (M + V)

This will give us the time intervals at which Vanya will meet his mother.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.