Question

Из города А и из города Б одновременно навстречу друг другу стартуют два велосипедиста со скоростями 9 км/ч и 11 км/ч соответственно. Одновременно ними из города А в город Б вылетает муха со скоростью 25 км/ч. Муха летит пока не встречает второго велосипедиста, после чего разворачивается и летит в противоположную сторону, пока не встретит первого велосипедиста, затем опять разворачивается и т.д. Муха летает до тех пор, пока велосипедисты не встретятся. Какое расстояние пролетит муха, если расстояние между городами 200 км?

Answer 1

1) 9 км/ч + 11 км/ч = 20 км/ч - скорость сближения велосипедистов.

2) 200 км : 20 км/ч = 10 ч - время движения велосипедистов (и столько же времени будет находиться в полёте муха).

3) 25 км/ч · 10 ч = 250 км - это расстояние, которое пролетит муха до тех пор, пока велосипедисты не встретятся.

Ответ: 250 км

Answer 2

Problem Analysis

We have two cyclists starting simultaneously from two different cities, A and B, towards each other. The first cyclist has a speed of 9 km/h, the second cyclist has a speed of 11 km/h, and a fly starts flying from city A towards city B with a speed of 25 km/h. The fly keeps flying until it meets the second cyclist, then it turns around and flies back towards the first cyclist, and so on. We need to find out how far the fly will fly before the two cyclists meet.

Solution

To solve this problem, we can calculate the time it takes for the two cyclists to meet and then use that time to find the distance the fly will fly.

Let's assume that the time it takes for the two cyclists to meet is t hours. Since they are moving towards each other, the total distance they cover is the sum of the distances covered by each cyclist. The distance covered by the first cyclist is 9t km, and the distance covered by the second cyclist is 11t km.

Since the fly is flying at a constant speed of 25 km/h, the distance it covers in t hours is 25t km.

To find the time it takes for the two cyclists to meet, we can use the formula:

Distance = Speed × Time

For the first cyclist: Distance = 9t km

For the second cyclist: Distance = 11t km

Since they are moving towards each other, the sum of their distances is equal to the total distance between the two cities, which is 200 km:

9t + 11t = 200

Simplifying the equation:

20t = 200

Dividing both sides by 20:

t = 10

So, it takes 10 hours for the two cyclists to meet.

Now, we can find the distance the fly will fly in 10 hours:

Distance = Speed × Time Distance = 25 km/h × 10 hours Distance = 250 km

Therefore, the fly will fly a distance of 250 km before the two cyclists meet.