Question

Первый велосипедист выехал из поселка по шоссе со скоростью 16 км ч.Через час после него со скоростью 12 км/ч из того же поселка в том же направлении выехал второй велосипедист. а еще через час после этого третий .найдите скорость третьего велосипедиста, если сначала он догнал второго ,а через 3 часа после длогнал первого

Answer 1

х - скорость 3-го велосипедиста, время движения его до встречи со 2-м - T.

Составим уравнения:

12(Т+1) = xТ

16(Т+5) = x(Т+3)

Решаем систему:

4(Т+5)/3(Т+1) = (Т+3)/Т, 

4Т^2 +20Т = 3Т^2 +12Т +9

Т^2 + 8Т – 9 = 0, t1 = 1, t2= -9

по Т1 находим,  x= 12(Т+1)/Т = 24 км/час

Answer 2

Problem Analysis

We are given the information about three cyclists who start from the same village and travel in the same direction. The first cyclist has a speed of 16 km/h, the second cyclist has a speed of 12 km/h, and the third cyclist starts one hour after the first cyclist. We need to find the speed of the third cyclist, given that they catch up to the second cyclist initially and then catch up to the first cyclist after three hours.

Solution

Let's analyze the problem step by step:

1. The first cyclist travels at a speed of 16 km/h for one hour. Therefore, the distance covered by the first cyclist in the first hour is 16 km.

2. After one hour, the second cyclist starts from the same village with a speed of 12 km/h. Since the second cyclist is starting one hour later, the first cyclist has already covered a distance of 16 km. To catch up to the first cyclist, the second cyclist needs to cover this distance.

3. The second cyclist is traveling at a speed of 12 km/h. To cover a distance of 16 km, the time taken by the second cyclist can be calculated using the formula: time = distance / speed. Therefore, the time taken by the second cyclist to catch up to the first cyclist is 16 km / 12 km/h = 4/3 hours.

4. Now, let's find the time it takes for the third cyclist to catch up to the first cyclist. We are given that the third cyclist catches up to the first cyclist after three hours. Since the second cyclist catches up to the first cyclist after 4/3 hours, the third cyclist catches up to the first cyclist after 3 - 4/3 = 5/3 hours.

5. Let's assume the speed of the third cyclist is v km/h. In 5/3 hours, the first cyclist travels a distance of 16 km/h * 5/3 hours = 80/3 km. The second cyclist travels a distance of 12 km/h * 5/3 hours = 20 km. The third cyclist catches up to the first cyclist after traveling a distance of 80/3 km - 20 km = 20/3 km.

6. Using the formula time = distance / speed, we can calculate the speed of the third cyclist. The time taken by the third cyclist to cover a distance of 20/3 km is 5/3 hours. Therefore, the speed of the third cyclist is (20/3 km) / (5/3 hours) = 20/5 = 4 km/h.

Answer

The speed of the third cyclist is 4 km/h.

Explanation

The first cyclist travels at a speed of 16 km/h for one hour, covering a distance of 16 km. The second cyclist starts one hour later and catches up to the first cyclist after traveling for 4/3 hours. The third cyclist catches up to the first cyclist after three hours and covers a distance of 20/3 km. Therefore, the speed of the third cyclist is 4 km/h.