Question

Из двух населённых пунктов навстречу друг другу вышли одновременно два лыжника.Скорость одного лыжника 8 км /ч, а скорость другого 9 км/ч. Через 4 часа лыжники встретились. Найди расстояние между селёнными пунктами. Реши задачу двумя способами

Answer 1

8+9 = 17км/ч
17*4=68км

Answer 2

Problem Statement

Два лыжника вышли из двух населенных пунктов навстречу друг другу одновременно. Скорость одного лыжника составляет 8 км/ч, а скорость другого - 9 км/ч. Через 4 часа лыжники встретились. Найдите расстояние между населенными пунктами и решите задачу двумя способами.

Solution 1: Using Relative Speed

To find the distance between the two towns, we can use the concept of relative speed. The relative speed is the sum of the speeds of the two skiers, as they are moving towards each other.

Let's denote the distance between the two towns as d.

The first skier's speed is 8 km/h, and the second skier's speed is 9 km/h. Since they are moving towards each other, their relative speed is 8 km/h + 9 km/h = 17 km/h.

In 4 hours, the skiers meet each other. We can use the formula distance = speed × time to find the distance traveled by each skier.

For the first skier: distance = speed × time = 8 km/h × 4 h = 32 km

For the second skier: distance = speed × time = 9 km/h × 4 h = 36 km

Since they meet each other, the sum of the distances traveled by both skiers should be equal to the distance between the two towns: 32 km + 36 km = 68 km

Therefore, the distance between the two towns is 68 km.

Solution 2: Using Time and Distance

Another way to solve this problem is by using the formula distance = speed × time for each skier.

Let's denote the distance between the two towns as d.

The first skier's speed is 8 km/h, and the second skier's speed is 9 km/h. Since they are moving towards each other, the total distance traveled by both skiers is equal to the distance between the two towns.

For the first skier: distance = speed × time = 8 km/h × 4 h = 32 km

For the second skier: distance = speed × time = 9 km/h × 4 h = 36 km

Since they meet each other, the sum of the distances traveled by both skiers should be equal to the distance between the two towns: 32 km + 36 km = 68 km

Therefore, the distance between the two towns is 68 km.

Conclusion

The distance between the two towns is 68 km. This can be calculated using either the concept of relative speed or by calculating the distance traveled by each skier using the formula distance = speed × time. Both methods yield the same result.