Question

В 14 часов 07 минут отряд русской конницы начал преследовать отряд противника , отступавший к переправе через Дунай со скоростью 180м/мин. В этот момент расстояние между ними было 495м. С какой скоростью должен был двигаться отряд русской конницы, чтобы догнать турков через 11 минут?

Answer 1

495:11=45(км/ч)

180+45=225(км/ч)

Answer 2

Answer in detail. At 14:07, a detachment of Russian cavalry began to pursue a detachment of the enemy, retreating to the crossing over the Danube at a speed of 180 m/min. At that moment, the distance between them was 495 m. At what speed should the detachment of Russian cavalry move to catch up with the Turks in 11 minutes?

This is a problem of uniform motion. To solve it, we need to use the formula for the distance traveled by a moving object: $$S = V \cdot t$$, where $$S$$ is the distance, $$V$$ is the speed, and $$t$$ is the time.

Let $$V_1$$ be the speed of the Russian cavalry, and $$V_2$$ be the speed of the enemy (180 m/min). Then, the relative speed of the Russian cavalry with respect to the enemy is $$V_1 - V_2$$.

We know that the distance between them at the start of the pursuit was 495 m, and the time of the pursuit was 11 minutes. Therefore, the distance covered by the Russian cavalry during the pursuit is $$495 + (V_1 - V_2) \cdot 11$$.

We also know that the Russian cavalry caught up with the enemy at the end of the pursuit, which means that the distance covered by the Russian cavalry was equal to the distance covered by the enemy. Therefore, we can write an equation:

$$495 + (V_1 - V_2) \cdot 11 = V_2 \cdot 11$$

Solving this equation for $$V_1$$, we get:

$$V_1 = V_2 + \frac{495}{11}$$

Substituting the value of $$V_2$$ (180 m/min), we get:

$$V_1 = 180 + \frac{495}{11}$$

$$V_1 = 180 + 45$$

$$V_1 = 225$$

Therefore, the speed of the Russian cavalry should be 225 m/min to catch up with the enemy in 11 minutes.