Question

От остановки электрички по тропинкам , расположенным перпендикулярно, одновременно отправились велосипедист Роман со скоростью 12км/ч и пешеход Вадим со скоростью 5 км/ч. Через какое время расстояние между Романом и Вадимом будет 26 км?

Answer 1

Расстояние между ними вычислим по теореме Пифагора - как  гипотенузу треугольника с катетами 12t  и 5t 
(сt)² = (12t)² + (5t)² = 169t²
ct = 13*t = 26 км  = Vc*t- расстояние совместного движения.
Находим время
t = 26 : 13 = 2 ч - время- ОТВЕТ

Answer 2

Problem Analysis

We are given that a cyclist named Roman and a pedestrian named Vadim start simultaneously from a train station and travel along perpendicular paths. Roman has a speed of 12 km/h, while Vadim has a speed of 5 km/h. We need to determine the time it takes for the distance between Roman and Vadim to be 26 km.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's assume that the time it takes for the distance between Roman and Vadim to be 26 km is t hours.

The distance traveled by Roman in t hours is given by: distance_Roman = speed_Roman × t.

Similarly, the distance traveled by Vadim in t hours is given by: distance_Vadim = speed_Vadim × t.

According to the problem, the distance between Roman and Vadim is 26 km. Therefore, we can write the equation:

distance_Roman - distance_Vadim = 26

Substituting the expressions for distance_Roman and distance_Vadim, we get:

(speed_Roman × t) - (speed_Vadim × t) = 26

Simplifying the equation, we have:

(speed_Roman - speed_Vadim) × t = 26

Now, we can substitute the given values for the speeds of Roman and Vadim:

(12 km/h - 5 km/h) × t = 26

Simplifying further, we have:

7 km/h × t = 26

To find the value of t, we can divide both sides of the equation by 7 km/h:

t = 26 km / 7 km/h

Calculating the value of t, we get:

t ≈ 3.714 hours

Therefore, it will take approximately 3.714 hours for the distance between Roman and Vadim to be 26 km.

Answer

The time it takes for the distance between Roman and Vadim to be 26 km is approximately 3.714 hours.