Question

Три велосипедиста из одного поселка в одном направлении выезжают с интервалом в 1 час. Первый двигался со скоростью12км/ч, второй - 10км/ч. Третий велосипедист, имея большую скорость, догнал второго, а еще через 2 часа догнал первого. Найти скорость третьего велосипедиста.

Answer 1

Прикрепляю......................

Answer 2

Problem Analysis

We are given the information about three cyclists who start from the same village in the same direction with a 1-hour interval. The first cyclist has a speed of 12 km/h, the second cyclist has a speed of 10 km/h, and the third cyclist, who has a higher speed, catches up with the second cyclist and then catches up with the first cyclist 2 hours later. We need to find the speed of the third cyclist.

Solution

Let's assume the speed of the third cyclist is v km/h.

To solve this problem, 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 v - 10 km/h. Similarly, the relative speed of the third cyclist with respect to the first cyclist is v - 12 km/h.

We are given that the third cyclist catches up with the second cyclist and then catches up with the first cyclist 2 hours later. This means that the time taken by the third cyclist to catch up with the second cyclist is the same as the time taken to catch up with the first cyclist.

Let's calculate the time taken by the third cyclist to catch up with the second cyclist and the first cyclist.

The time taken by the third cyclist to catch up with the second cyclist can be calculated using the formula:

Distance = Speed × Time

The distance covered by the second cyclist in this time is 10 × 2 km.

The time taken by the third cyclist to catch up with the first cyclist can be calculated using the formula:

Distance = Speed × Time

The distance covered by the first cyclist in this time is 12 × 4 km.

Since the distances covered by the third cyclist to catch up with the second cyclist and the first cyclist are the same, we can equate the two distances:

(v - 10) × 2 = (v - 12) × 4

Let's solve this equation to find the value of v.

(v - 10) × 2 = (v - 12) × 4

Simplifying the equation:

2v - 20 = 4v - 48

2v - 4v = -48 + 20

-2v = -28

v = 14

Therefore, the speed of the third cyclist is 14 km/h.

Answer

The speed of the third cyclist is 14 km/h.