Question

составить математическую модель ситуации: из пункта А в пункт В одновременно вышли 2 пешехода: 1 со скоростью 6 км/ч, второй - 4 км/ч. через 30 минут после этого вслед за ними выехал велосипедист, который обогнал первого пешехода за 20 минут после того, как обогнал другого

Answer 1

Скорость велосипедиста - V.

На момент выезда велосипедиста, первый пешеход прошёл 6*0,5 = 3 км, второй - 4*0,5 = 2 км.

Пусть велосипедист обогнал второго пешехода через t мин. За это время велосипедист проехал t*V км, 2ой пешеход прошёл 2+4t км. Оба они преодолели одинаковое расстояние, т.е. t*V = 2+4t.

Велосипедист обогнал первого пешехода через 20 минут после второго, т.е. в пути он находился t+1/3 мин, проехав расстояние (t+1/3)*V. Первый пешеход на этот момент прошёл 3+6(t+1/3) км. Оба преодолели одно и то же расстояние, т.е. (t+1/3)*V = 3+6(t+1/3).

Мат.моделью задачи будет система из 2х уравнений с 2мя неизвестными:

$\\\begin{cases}t\cdot V = 2+4t\\(t+1/3)\cdot V=3+6(t+1/3)\end{cases}$

Answer 2

Mathematical Model of the Situation

To create a mathematical model of the situation, let's define the following variables: - Distance from point A to point B: S - Speed of the first pedestrian: v1 = 6 km/h - Speed of the second pedestrian: v2 = 4 km/h - Time it takes for the first pedestrian to reach point B: t1 = S / v1 - Time it takes for the second pedestrian to reach point B: t2 = S / v2 - Time it takes for the cyclist to catch up with the first pedestrian: t3 = t1 + 30 minutes - Time it takes for the cyclist to catch up with the second pedestrian: t4 = t2 + 30 minutes

Based on the given information, we can derive the following equations:

1. Distance traveled by the first pedestrian: d1 = v1 * t1 2. Distance traveled by the second pedestrian: d2 = v2 * t2 3. Distance traveled by the cyclist when catching up with the first pedestrian: d3 = v1 * t3 4. Distance traveled by the cyclist when catching up with the second pedestrian: d4 = v2 * t4

We also know that the cyclist catches up with the first pedestrian 20 minutes after catching up with the second pedestrian. This can be expressed as:

5. Time difference between catching up with the first and second pedestrian: t4 - t3 = 20 minutes

Now, let's solve the equations to find the values of the variables.

Solution

1. From equation 1, we have: d1 = v1 * t1 2. From equation 2, we have: d2 = v2 * t2 3. From equation 3, we have: d3 = v1 * t3 4. From equation 4, we have: d4 = v2 * t4 5. From equation 5, we have: t4 - t3 = 20 minutes

To find the values of t1, t2, t3, and t4, we need to eliminate the distances d1, d2, d3, and d4.

From the given information, we know that the cyclist catches up with the first pedestrian 20 minutes after catching up with the second pedestrian. This means that the distance traveled by the cyclist when catching up with the first pedestrian is equal to the distance traveled by the cyclist when catching up with the second pedestrian plus the distance between the two pedestrians.

Mathematically, this can be expressed as:

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