Question

Два велосипедиста участвуют в гонках по круговой дорожке. Первый велосипедист проходит круг за 6 минут, второй за 4 минуты. Через какое время второй велосипедист догонит первого? Нужно полное решение

Answer 1

Гонка по кругу - когда велосипедисты стартуют на противоположных сторонах круга и догоняют друг друга. Скорость одного 1/4 круг/мин второго 1/6 кр/мин. Скорость сближения Vсб =1/4-1/6 = 1/12. Значит второй догонит первого через 12 минут.

Answer 2

To find out when the second cyclist will catch up to the first cyclist, we can use the concept of relative speed. The relative speed is the difference in speeds between the two cyclists.

Let's assume that the length of the circular track is L. Since the first cyclist completes one lap in 6 minutes, their speed is L/6. Similarly, the second cyclist completes one lap in 4 minutes, so their speed is L/4.

Now, let's consider the time it takes for the second cyclist to catch up to the first cyclist. Let's call this time T.

During this time T, the first cyclist will have completed T/6 laps, and the second cyclist will have completed T/4 laps. Since the second cyclist catches up to the first cyclist, the distance covered by both cyclists must be the same.

Therefore, we can set up the equation:

(T/6) * (L) = (T/4) * (L)

Simplifying the equation, we can cancel out the L:

T/6 = T/4

To solve for T, we can cross-multiply:

4T = 6T

2T = 0

Since this equation has no solution, it means that the second cyclist will never catch up to the first cyclist. This is because the second cyclist is faster than the first cyclist, and therefore, they will never be at the same position on the circular track.

Therefore, the second cyclist will not be able to catch up to the first cyclist.

I hope this explanation helps! Let me know if you have any further questions.