Question

Пешеход и велосипедист одновременно отправляются из одной точки по шоссе навстречу мотоциклисту. Все трое движутся с постоянными скоростями. В тот момент, когда велосипедист встретил мотоциклиста, пешеход отставал от велосипедиста на 3 км. В тот момент, когда пешеход встретил мотоциклиста, велосипедист обогнал пешехода на 6 км. Какое расстояние было между пешеходом и мотоциклистом в момент отправления пешехода?

Answer 1

Скорости: мотоциклист(М) = х км/ч, велосипедист(В) =y км/ч, пешеход(П)= z км/ч.

Время: от встречи П и В, до М и В = t1 часов; от встерчи П и В до П и М = t2 часов.

 

Зная, что S=v*t, составим и решим систему уравнений:

 

Разделим первое уравнение на второе b третье на четвертое.

Получим:

 

 

Отсюда S=2 км

 

Ответ: 2 км

Answer 2

Problem Analysis

We have a pedestrian, a cyclist, and a motorcyclist all starting from the same point on a highway and moving towards each other. The pedestrian is initially 3 km behind the cyclist, and when the pedestrian meets the motorcyclist, the cyclist has already passed the pedestrian by 6 km. We need to find the distance between the pedestrian and the motorcyclist at the moment the pedestrian starts.

Solution

Let's assume the speed of the pedestrian is P km/h, the speed of the cyclist is C km/h, and the speed of the motorcyclist is M km/h.

When the pedestrian meets the motorcyclist, the cyclist has already passed the pedestrian by 6 km. This means that the time it takes for the cyclist to pass the pedestrian is equal to the time it takes for the pedestrian to meet the motorcyclist.

Let's denote the time it takes for the pedestrian to meet the motorcyclist as t hours.

At time t, the pedestrian has traveled a distance of P * t km, and the cyclist has traveled a distance of C * t km.

According to the problem, the pedestrian is initially 3 km behind the cyclist. So we can write the following equation:

P * t = C * t + 3 (Equation 1)

When the pedestrian meets the motorcyclist, the cyclist has already passed the pedestrian by 6 km. So we can write another equation:

C * t = P * t + 6 (Equation 2)

We can solve this system of equations to find the values of P, C, and t.

Solving the Equations

Let's solve the system of equations (Equation 1 and Equation 2) to find the values of P, C, and t.

From Equation 1, we can rewrite it as:

P * t - C * t = 3 (Equation 3)

From Equation 2, we can rewrite it as:

C * t - P * t = 6 (Equation 4)

Adding Equation 3 and Equation 4, we get:

(P * t - C * t) + (C * t - P * t) = 3 + 6

Simplifying the equation, we get:

0 = 9

This equation is not possible, which means there is no solution for the system of equations. Therefore, we cannot determine the values of P, C, and t.

Since we cannot determine the values of P, C, and t, we cannot calculate the distance between the pedestrian and the motorcyclist at the moment the pedestrian starts.

Conclusion

Based on the given information, we cannot determine the distance between the pedestrian and the motorcyclist at the moment the pedestrian starts. The system of equations does not have a solution, so we cannot find the values of the speeds and time required to calculate the distance.