Question

Два велосипедиста выехали навстречу друг другу по одной и той же дороге, соединяющей два села одному на весь путь требуется 1 час , а другому - полтора часа. Через сколько минут они встретятся ?

Answer 1

Расстояние между сёлами х .где х сорость одного велосипедиста

х/1,5 скорость второго велосипедиста

х/(х+х/1,5)=3/5 часа или через 36 минут велосипедисты встретятся

Answer 2

Answer in detail. Two cyclists set out to meet each other on the same road, connecting two villages. One takes 1 hour for the whole journey, and the other takes one and a half hours. How many minutes will they meet?

This is a problem of relative speed and distance. Let us assume that the distance between the two villages is D kilometers, and the speeds of the cyclists are V1 and V2 kilometers per hour, respectively. Then, we can write the following equations:

$$D = V1 \times 1$$ $$D = V2 \times 1.5$$

Solving for V1 and V2, we get:

$$V1 = D$$ $$V2 = \frac{2}{3}D$$

Now, let us consider the situation when the cyclists start moving towards each other. The relative speed of the cyclists is the sum of their individual speeds, which is:

$$V_{rel} = V1 + V2 = D + \frac{2}{3}D = \frac{5}{3}D$$

The relative distance between the cyclists is the same as the distance between the villages, which is D. Therefore, the time taken for the cyclists to meet each other is the ratio of the relative distance and the relative speed, which is:

$$T = \frac{D}{V_{rel}} = \frac{D}{\frac{5}{3}D} = \frac{3}{5}$$

This is the time in hours. To convert it to minutes, we multiply it by 60, which gives:

$$T = \frac{3}{5} \times 60 = 36$$

Therefore, the cyclists will meet each other after 36 minutes.