Question

Чтобы попасть на место в заданное время, Емеля пошел из деревни со скоростью v1 = 5 км/ч. Начался сильный снегопад, и он снизил скорость до v2 = 3 км/ч. Когда снегопад кончился, Емеля продолжил идти со скоростью v1. В результате, в город он прибыл на 30 мин позже запланированного. Сколько времени шел снегопад?

Answer 1

35 минут шел снегопад

Answer 2

Problem Analysis

To solve this problem, we need to determine the duration of the snowfall. We are given the initial speed of Emelya, the reduced speed during the snowfall, and the delay in his arrival at the destination. By calculating the time it took Emelya to reach the city without the snowfall and comparing it to the actual time, we can find the duration of the snowfall.

Solution

Let's assume that the distance from the village to the city is d kilometers.

1. Without the snowfall, Emelya traveled from the village to the city at a speed of v1 = 5 km/h. The time it took him to cover the distance is given by the formula: time1 = d / v1.

2. During the snowfall, Emelya reduced his speed to v2 = 3 km/h. The time it took him to cover the same distance is given by the formula: time2 = d / v2.

3. After the snowfall, Emelya resumed his original speed of v1 = 5 km/h. The time it took him to cover the distance is given by the formula: time3 = d / v1.

4. According to the problem, Emelya arrived at the city 30 minutes later than planned. Since we know that time1 + time2 + time3 = planned time + 30 minutes, we can substitute the formulas for time1, time2, and time3 to get: d / v1 + d / v2 + d / v1 = planned time + 30 minutes.

5. We can simplify the equation by multiplying both sides by the least common multiple (LCM) of v1 and v2, which is 15: 15 * (d / v1) + 15 * (d / v2) + 15 * (d / v1) = 15 * (planned time + 30 minutes).

6. Simplifying further, we get: 15 * (2d / v1 + d / v2) = 15 * (planned time + 30 minutes).

7. Canceling out the common factors, we have: 2d / v1 + d / v2 = planned time + 30 minutes.

8. Rearranging the equation, we get: 2d / v1 = planned time + 30 minutes - d / v2.

9. Solving for d, we find: d = (v1 * (planned time + 30 minutes)) / (2 - (v1 / v2)).

10. Finally, we can calculate the duration of the snowfall by substituting the values of v1, v2, and the planned time into the formula for d.

Let's calculate the duration of the snowfall using the given values.

Calculation

Given: - v1 = 5 km/h - v2 = 3 km/h - Delay = 30 minutes

Substituting the values into the formula for d, we get: d = (5 * (planned time + 30 minutes)) / (2 - (5 / 3)).

Since the planned time is not provided in the question, we cannot calculate the exact duration of the snowfall without that information.

Please provide the planned time, and I will be able to calculate the duration of the snowfall for you.