Question

Пожалуйста, помогите!!! Если можно, то на листочке Первый велосепедист выехал из поселка по шосс со скоростью 12 км/ч. Через час после него со скоростью 10 км/ч из того же поселка в том же направлении выехал второй велосипедист, а еще через час третий. Найдите скорость третьего велосепедистп, если сначала он догнал второго, а через 2 часа поосле этого догнал первого.

Answer 1

скорость 3-го велосипедиста х ( она самая высокая)

 его путь tx (  так как он догнал 2-го через t  часов)

   путь 2 -го   велосепедиста 10 (t+1) км ( он ехал t+1 часов)

tx = 10(t+1)     (1)

 Путь , который проехал 3 ий велосепедист x(t+2) ( время в пути t+2) и  догнал первого. , а первый проехал 12( t+4). 

tx = 10(t+1)     (1)

x(t+2) = 12(t+4) >>tx+2х=12t +48    (2)  

Решим систему уравнений 

tx из(1) подставим в (2) :

10(t+1)+2х=12t+48

10t+10+2x=12t+48

2t=2x-38

t=x-19  подставим t в (1)

(х-19)*х=10(х-19+1)

х²-19х=10-180

х²-29х+180=0

Д=121  √Д=11

х1=(29+11):2=20  км /час  скорость 3 его

х2=(29-11):2=9 не подходит по условию

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 starts with a speed of 12 km/h, the second cyclist starts one hour later with a speed of 10 km/h, and the third cyclist starts two hours after the first cyclist. We need to find the speed of the third cyclist, given that they first catch up to the second cyclist and then catch up to the first cyclist two hours later.

Solution

Let's break down the problem step by step:

1. Let's assume the speed of the third cyclist is v km/h. 2. The first cyclist travels for one hour at a speed of 12 km/h, so they cover a distance of 12 km. 3. The second cyclist starts one hour later and travels at a speed of 10 km/h. By the time the second cyclist starts, the first cyclist has already covered a distance of 12 km. To catch up to the first cyclist, the second cyclist needs to cover this distance. The time taken by the second cyclist to cover this distance is given by the formula: time = distance / speed. Therefore, the time taken by the second cyclist to catch up to the first cyclist is 12 km / 10 km/h = 1.2 hours. 4. Now, the third cyclist starts two hours after the first cyclist. By the time the third cyclist starts, the first cyclist has already covered a distance of 12 km, and the second cyclist has caught up to the first cyclist. To catch up to both the first and second cyclists, the third cyclist needs to cover a distance of 12 km. The time taken by the third cyclist to cover this distance is given by the formula: time = distance / speed. Therefore, the time taken by the third cyclist to catch up to both the first and second cyclists is 12 km / v km/h = 2 hours. 5. From step 4, we can write the equation: 12 km / v km/h = 2 hours. Solving this equation for v, we get v = 6 km/h.

Therefore, the speed of the third cyclist is 6 km/h.

Answer

The speed of the third cyclist is 6 km/h.