Question

Реши задачу разными способами из двух поселков находятся находятся друг от друга на расстоянии 17 км одновременно в противоположнойнаправленияз вышли два лыжника. через некоторое время они остановились. в тот момент расстояние между ними было равно 110 км. скорость первого лыжника равна 14 км ч а скорость второго 17 км ч через сколько часов лыжники остановились

Answer 1

110-17=93(км)они проехали от друг друга
17+14=31(км)скорость отдаления
93÷31=3(ч)

Answer 2

Problem Analysis

We have two skiers who start from two different villages simultaneously and move in opposite directions. After some time, they stop, and at that moment, the distance between them is 110 km. The speed of the first skier is 14 km/h, and the speed of the second skier is 17 km/h. We need to find out how many hours it took for the skiers to stop.

Solution 1: Using Relative Speed

To solve this problem, we can consider the relative speed of the skiers. The relative speed is the difference between their individual speeds. Let's assume that the skiers stopped after t hours.

The distance covered by the first skier in t hours is given by: Distance1 = Speed1 × Time = 14t

Similarly, the distance covered by the second skier in t hours is given by: Distance2 = Speed2 × Time = 17t

Since they are moving in opposite directions, the total distance between them is the sum of the distances covered by each skier: Total Distance = Distance1 + Distance2 = 14t + 17t = 31t

According to the problem, the total distance between them when they stopped was 110 km. Therefore, we can set up the equation: 31t = 110

To find the value of t, we can solve this equation: t = 110 / 31

Now, let's calculate the value of t.

Calculation

t = 110 / 31 = 3.548

Therefore, the skiers stopped after approximately 3.548 hours.

Solution 2: Using Distance Formula

Another way to solve this problem is by using the distance formula. We know that the distance between the skiers is 110 km, and their speeds are 14 km/h and 17 km/h. Let's assume that the skiers stopped after t hours.

The distance covered by the first skier in t hours is given by: Distance1 = Speed1 × Time = 14t

Similarly, the distance covered by the second skier in t hours is given by: Distance2 = Speed2 × Time = 17t

The total distance between them when they stopped is given by: Total Distance = Distance1 + Distance2 = 14t + 17t = 31t

According to the problem, the total distance between them when they stopped was 110 km. Therefore, we can set up the equation: 31t = 110

To find the value of t, we can solve this equation: t = 110 / 31

Now, let's calculate the value of t.

Calculation

t = 110 / 31 = 3.548

Therefore, the skiers stopped after approximately 3.548 hours.

Conclusion

Both solutions yield the same result. The skiers stopped after approximately 3.548 hours.