Question

Два бегуна одновременно стартовали в одном направлении из одного и того же места круговой трассы в беге на несколько кругов спустя один час когда одному из них оставалось 2 км до окончания первого круга ему сообщили, что второй бегун пробежал первый круг 9 минут назад найдите скорость первого бегуна если известно что она на 5 км ч меньше скорости второго

Answer 1

Первый бегун:
Скорость - х км/час;
Время - 1 час 
Расстояние, которое он пробежал  -   1* х   км 
Длина дорожки (1 круга) -  (х+2 ) км

Второй бегун:
Скорость   - ( х+5) км / час.
Время  -    (1- 9/60) = (1-3/20)= 17/20 часа
Расстояние =длине дорожки  -  17/20 * (х+5)   км

Уравнение:
х+2= 17/20 * (х+5)
х+2= 17/20 *х + 17/20 * 5 
х - 17/20 *х  =  17/4 - 2 
х*( 1- 17/20) = 4  1/4 - 2
3/20 х = 2  1/4
х= 2  1/4   : 3/20 = 9/4  * 20/3 = (3*5)/(1*1)
х= 15 км /ч  - скорость первого бегуна.

Ответ: 15 км/ч скорость первого бегуна.

Answer 2

15 км\ч скорость первого бегуна

Answer 3

Problem Analysis

Two runners start simultaneously from the same point on a circular track and run for several laps. After one hour, when one of them has 2 km left to complete the first lap, they are informed that the second runner completed the first lap 9 minutes ago. We need to find the speed of the first runner, given that it is 5 km/h slower than the speed of the second runner.

Solution

Let's assume the speed of the second runner is x km/h. Therefore, the speed of the first runner is x - 5 km/h.

We know that the second runner completed the first lap 9 minutes ago. Since the first runner has 2 km left to complete the first lap, we can calculate the time it took for the second runner to complete the first lap.

The time taken to complete the first lap by the second runner is given by the formula:

Time = Distance / Speed

The distance is the circumference of the circular track, which is equal to the length of one lap. We can calculate the length of one lap using the formula:

Length of Lap = 2 * π * Radius

Since we don't have the radius of the circular track, we can assume it to be 1. This assumption will not affect the relative speeds of the runners.

Now, let's calculate the length of one lap and the time taken by the second runner to complete the first lap.

Calculation

Length of Lap = 2 * π * 1 = 2π km

Time taken by the second runner to complete the first lap = 9 minutes = 9/60 hours = 0.15 hours

Now, we can calculate the speed of the first runner using the formula:

Speed = Distance / Time

The distance is the remaining 2 km to complete the first lap, and the time is 1 hour.

Calculation

Speed of the first runner = 2 km / 1 hour = 2 km/h

Therefore, the speed of the first runner is 2 km/h.

Answer

The speed of the first runner is 2 km/h.

Explanation

The first runner has a slower speed compared to the second runner. The second runner completed the first lap 9 minutes ago, which means the first runner is slower and still has 2 km left to complete the first lap.