Question

Первый велосипедист выехал из посёлка по шоссе со скоростью 20 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 8 часов после этого догнал первого.

Answer 1

Пусть его скорость была -Хкм/ч.
Первый за 2 часа проехал  16*2=32 км,
  что бы его догнать нужно 32/(Х-16) часов.
Второй за 1 час проехал 10 км,
  что бы догнать второго нужно 10/(Х-10) часов.
Разница в гонке между ними известно по условию.
Состовляем уравнение
32/(Х-16)-10/(Х-10)=4,5
32Х-320-10Х+160=4,5(Х-10)(Х-16) при Х≠10 и Х≠16
22Х-160=4,5(Х²-26Х+160)
4,5Х²-139Х+880=0
Д=59²
Х1=(139+59)/9=22
Х2=(139-59)/9=8.(8)
Так как Х2<10 то это не может быть решением,
так как он никогда не догнал бы даже второго велосипедиста.
Получаем ответ при Х=22км/ч
  Ответ: 22 км/ч

Answer 2

Problem Analysis

We are given the following information: - The first cyclist starts from a village on a highway with a speed of 20 km/h. - One hour later, the second cyclist starts from the same village in the same direction with a speed of 16 km/h. - Another hour later, the third cyclist starts from the same village in the same direction.

We need to find the speed of the third cyclist if they first catch up to the second cyclist and then catch up to the first cyclist 8 hours later.

Solution

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

To find the speed of the third cyclist, we can set up the following equations:

1. When the third cyclist catches up to the second cyclist: - The second cyclist has been cycling for 2 hours (1 hour before the third cyclist starts and 1 hour after). - The distance covered by the second cyclist is 16 km/h * 2 h = 32 km. - The distance covered by the third cyclist is x km/h * 2 h. - Since they cover the same distance, we can set up the equation: x km/h * 2 h = 32 km.

2. When the third cyclist catches up to the first cyclist: - The first cyclist has been cycling for 9 hours (1 hour before the second cyclist starts and 8 hours after). - The distance covered by the first cyclist is 20 km/h * 9 h = 180 km. - The distance covered by the third cyclist is x km/h * 9 h. - Since they cover the same distance, we can set up the equation: x km/h * 9 h = 180 km.

Now we have a system of two equations with two unknowns. We can solve this system to find the value of x.

Solving the System of Equations

Let's solve the system of equations:

Equation 1: x km/h * 2 h = 32 km Equation 2: x km/h * 9 h = 180 km

To solve this system, we can divide Equation 2 by Equation 1:

(x km/h * 9 h) / (x km/h * 2 h) = 180 km / 32 km Simplifying, we get:

9 h / 2 h = 180 km / 32 km 4.5 = 5.625

This equation is not true, which means there is no solution. It seems there is an error in the problem statement or the given information.

Unfortunately, we cannot determine the speed of the third cyclist with the given information.

Please let me know if there is anything else I can help you with.