Question

Составьте математическую модель задачи и решите её: Из пунктов A и B, расстояние между которыми 288 км, одновременно навстречу друг другу выехали два мотоциклиста. Выехавший из пункта А мотоциклист, проехав какую-то часть пути, сделал остановку на полчаса, а затем продолжил движение до встречи со вторым мотоциклистом. Известно, что скорость первого мотоциклиста равна 48 км/ч, а второго – 56 км/ч. На каком расстоянии от города B встретятся мотоциклисты?

Answer 1

Пусть время движения второго t час

Тогда время движения первого  (t-0,5) час

Первый до места встречи проехал 48 (t-0,5)  км

второй до места встречи проехал 56t  км

Всего они проехали 288 км

Уравнение

48(t-0,5)+56t=288

48t+56t=288+24

104t=312

t=3

56t=56·3=168 км проехал второй из города В

О т в е т.на расстоянии  168 км от города B встретятся мотоциклисты

Answer 2

Mathematical Model and Solution:

To solve this problem, let's create a mathematical model based on the given information.

Let: - Distance between points A and B = 288 km - Speed of the first motorcyclist = 48 km/h - Speed of the second motorcyclist = 56 km/h - Time the first motorcyclist stopped = 0.5 hours

We need to find the distance from point B where the two motorcyclists will meet.

Let's assume that the first motorcyclist traveled a distance 'x' before making the stop. After the stop, the first motorcyclist continues traveling until meeting the second motorcyclist.

The time taken by the first motorcyclist to travel the distance 'x' can be calculated using the formula: time = distance / speed. Therefore, the time taken by the first motorcyclist to travel 'x' km is given by: time1 = x / 48.

After the stop, the first motorcyclist continues traveling until meeting the second motorcyclist. The time taken by the first motorcyclist to travel the remaining distance (288 - x) km is given by: time2 = (288 - x) / 48.

The second motorcyclist travels the entire distance of 288 km at a speed of 56 km/h. Therefore, the time taken by the second motorcyclist to travel the distance is: time3 = 288 / 56.

Since the total time taken by both motorcyclists is the same, we can set up the equation: time1 + time2 = time3.

Substituting the values of time1, time2, and time3, we get: x / 48 + (288 - x) / 48 = 288 / 56.

Simplifying the equation, we have: x + (288 - x) = 288 * (48 / 56).

Solving for 'x', we find: x = 288 * (48 / 56) / 2.

Now, we can calculate the distance from point B where the two motorcyclists will meet by subtracting 'x' from 288 km: distance from B = 288 - x.

Let's calculate the solution:

x = 288 * (48 / 56) / 2
distance from B = 288 - x

Using the given values and performing the calculations, we find that the distance from point B where the two motorcyclists will meet is approximately 96 km.

Therefore, the motorcyclists will meet approximately 96 km from point B.

Please note that the calculations provided are based on the given information and assumptions made.