Question

Из двух посёлков, расстояние между которыми равно 27,4 км, выехали на встречу друг другу 2 велосепедиста со скоростями 12,5 км/ч и 14км/ч. Проехав 5 км, первый велосепелист встретил второго. На сколько часов позже, чем второй велосипедист, он выехал из посёлка?

Answer 1

1)5:12.5=0.4ч-время в пути первого.

2)27.4-5=22.4км-проехал второй.

3)22.4:14=1.6ч-время в пути второго.

4)1.6-0.4=на 1.2часа позже-выехал первый велосипедист.

 

Answer 2

Problem Analysis

We have two cyclists who start from two different villages and are traveling towards each other. The distance between the villages is 27.4 km. The first cyclist has a speed of 12.5 km/h, and the second cyclist has a speed of 14 km/h. After traveling 5 km, the first cyclist meets the second cyclist. We need to determine how many hours later the first cyclist left his village compared to the second cyclist.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the two cyclists is the sum of their individual speeds. We can calculate the time it takes for the two cyclists to meet by dividing the distance between the villages by their relative speed. Since the first cyclist has already traveled 5 km, we can subtract this distance from the total distance to find the remaining distance that the second cyclist needs to cover. Finally, we can calculate the time it takes for the second cyclist to cover this remaining distance using their speed.

Let's calculate the solution step by step:

1. Calculate the relative speed of the two cyclists: - First cyclist's speed: 12.5 km/h - Second cyclist's speed: 14 km/h - Relative speed: 12.5 km/h + 14 km/h = 26.5 km/h

2. Calculate the time it takes for the two cyclists to meet: - Distance between the villages: 27.4 km - Time = Distance / Speed = 27.4 km / 26.5 km/h = 1.034 hours

3. Calculate the remaining distance for the second cyclist: - Distance traveled by the first cyclist: 5 km - Remaining distance = Total distance - Distance traveled by the first cyclist = 27.4 km - 5 km = 22.4 km

4. Calculate the time it takes for the second cyclist to cover the remaining distance: - Speed of the second cyclist: 14 km/h - Time = Distance / Speed = 22.4 km / 14 km/h = 1.6 hours

5. Calculate the time difference between the two cyclists: - Time difference = Time taken by the second cyclist - Time taken by the first cyclist = 1.6 hours - 1.034 hours = 0.566 hours

Answer

The first cyclist left his village 0.566 hours (approximately 34 minutes) later than the second cyclist.

Verification

Let's verify the solution using the given information and calculations:

- The relative speed of the two cyclists is 26.5 km/h. - The time it takes for the two cyclists to meet is approximately 1.034 hours. - The remaining distance for the second cyclist is approximately 22.4 km. - The time it takes for the second cyclist to cover the remaining distance is approximately 1.6 hours. - The time difference between the two cyclists is approximately 0.566 hours.

The solution is consistent with the given information and calculations.