Question

Из пункта А в пункт В выехала автомашина с постоянной скоростью 80 км/ч. Спустя 15 мин из пункта В в пункт А выехал велосипедист с постоянной скоростью 20 км/ч. Найдите место и время встречи автомашины и велосипедиста, если расстояние между пунктами А и В равно 55 км.

Answer 1

 дано: 
V01 = 80км/ч
V02 = 20км/ч
S0 = 55 км
t0 = 15мин
Тогда законы будут следующие.
Автомашина:
S = V*t = V01 * t
Велосипедист:
S = S0 - V*(t - t0) = S0 - V02 * (t - t0)
Замечу, что в вышеприведенных уравнениях t и S - параметры.
1) находим место встречи аналитически.
Встреча означает, что S равны. То есть:
S0 - V02 * (t - t0) = V01 * t
55 - 20 (t - 0,25) = 80t
100t = 50
t = 0,5 ч = 30 мин.
2) Графически.
Необходимо нарисовать графики функций, приведенных вначале, где t - аргумент (шкала х), S - функция (шкала у). Точка их пересечения - момент встречи

Answer 2

Problem Analysis

We are given that a car travels from point A to point B at a constant speed of 80 km/h, and after 15 minutes, a cyclist starts from point B to point A at a constant speed of 20 km/h. We need to find the meeting point and time between the car and the cyclist, given that the distance between points A and B is 55 km.

Solution

Let's start by converting the time of the car's departure into hours. Since 15 minutes is equivalent to 0.25 hours, the car starts its journey 0.25 hours after the cyclist.

Next, we can calculate the distance covered by the car during this time. The car's speed is 80 km/h, and it travels for 0.25 hours, so the distance covered by the car is:

Distance covered by the car = Car's speed * Time = 80 km/h * 0.25 h = 20 km.

Now, we can calculate the remaining distance between the car and the cyclist. The total distance between points A and B is 55 km, and the car has already covered 20 km. Therefore, the remaining distance is:

Remaining distance = Total distance - Distance covered by the car = 55 km - 20 km = 35 km.

Since both the car and the cyclist are moving towards each other, their combined speed is the sum of their individual speeds. The combined speed is:

Combined speed = Car's speed + Cyclist's speed = 80 km/h + 20 km/h = 100 km/h.

To find the time of their meeting, we can use the formula:

Time = Distance / Combined speed = 35 km / 100 km/h.

Now, let's calculate the time of their meeting:

Time = 0.35 hours.

Therefore, the car and the cyclist will meet after 0.35 hours, or 21 minutes, from the car's departure time.

To find the meeting point, we can calculate the distance covered by the car during this time:

Distance covered by the car = Car's speed * Time = 80 km/h * 0.35 h = 28 km.

Since the car has already covered 20 km, the meeting point will be:

Meeting point = Distance covered by the car + Distance already covered by the car = 28 km + 20 km = 48 km.

Therefore, the car and the cyclist will meet at a distance of 48 km from point A.

Answer

The car and the cyclist will meet at a distance of 48 km from point A. The meeting will occur 21 minutes after the car's departure time.

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