Question

Пер­вый ве­ло­си­пе­дист вы­ехал из посёлка по шоссе со ско­ро­стью 18 км/ч. Через час после него со ско­ро­стью 16 км/ч из того же посёлка в том же на­прав­ле­нии вы­ехал вто­рой ве­ло­си­пе­дист, а ещё через час — тре­тий. Най­ди­те ско­рость тре­тье­го ве­ло­си­пе­ди­ста, если сна­ча­ла он до­гнал вто­ро­го, а через 4 часа после этого до­гнал пер­во­го.

Answer 1

Problem Analysis

We are given the information about three cyclists who start from the same village, one after the other, and travel at different speeds. We need to find the speed of the third cyclist, who catches up to the second cyclist and then catches up to the first cyclist after 4 hours.

Solution

Let's break down the problem step by step:

1. The first cyclist travels at a speed of 18 km/h. 2. After 1 hour, the second cyclist starts from the same village and travels at a speed of 16 km/h. 3. After another hour (2 hours in total), the third cyclist starts from the same village and catches up to the second cyclist. 4. After 4 hours from the start of the third cyclist (6 hours in total), the third cyclist catches up to the first cyclist.

To find the speed of the third cyclist, we can use the concept of relative speed. The relative speed of the third cyclist with respect to the second cyclist is the difference in their speeds, which is 18 km/h - 16 km/h = 2 km/h.

Now, let's calculate the distance covered by the third cyclist in 4 hours. Since the third cyclist catches up to the first cyclist after 4 hours, the distance covered by the third cyclist is the same as the distance between the first and second cyclists.

The distance covered by the first cyclist in 4 hours is 18 km/h * 4 hours = 72 km.

Therefore, the speed of the third cyclist is the distance covered (72 km) divided by the time taken (4 hours), which is 18 km/h.

Answer

The speed of the third cyclist is 18 km/h.