Question

Города А,В и С соединены прямолинейным шоссе,причем город В расположен между городами А и С. Из города А в сторону города С выехал легковой автомобиль и одновременно с ним из города В в сторону города С выехал грузовик. Через сколько часов после выезда легковой автомобиль догонит грузовик,если скорость легкового автомобиля на 25 км/ч больше скорости грузовика,а расстояние между городами А и В равно 125 км?

Answer 1

Способ 1 (через уравнение):
Пусть х ч - время в пути автомобилей, заполним таблицу

                              скорость       время          расстояние
легковое авто       +25 км/ч    х  (ч) одинак            + 125 км
грузовой а/м                           х  (ч) одинак    
отметим, что разность в скоростях автомобилей по условию задачи равна 25 км/ч. Составляем уравнение по условию задачи:

25х = 125
х= 125: 25
х= 5 ч  - время в пути до встречи каждого автомобиля.

Способ 2 (по действиям):
25 км/ч - скорость сближения
125 км - разность в пройденных расстояниях
1) 125 : 25 = 5 ч - время в пути каждого автомобиля до встречи

Answer 2

Problem Analysis

We are given three cities, A, B, and C, connected by a straight highway. City B is located between cities A and C. A car leaves city A towards city C at the same time a truck leaves city B towards city C. The car's speed is 25 km/h faster than the truck's speed. The distance between cities A and B is 125 km. We need to determine how many hours after the car's departure it will catch up to the truck.

Solution

Let's denote the speed of the truck as x km/h. Since the car's speed is 25 km/h faster, the car's speed is x + 25 km/h.

To find the time it takes for the car to catch up to the truck, we need to determine the distance the car needs to travel to reach the truck. Since the truck has a head start, the distance the car needs to travel is the total distance between cities A and C minus the distance between cities A and B.

The total distance between cities A and C is not given directly, but we can calculate it using the distance between cities A and B and the distance between cities B and C.

Let's denote the distance between cities B and C as d km. The distance between cities A and C is then 125 + d km.

Now we can calculate the time it takes for the car to catch up to the truck using the formula:

time = distance / speed

Substituting the values we have:

time = (125 + d) / (x + 25)

Therefore, the car will catch up to the truck after (125 + d) / (x + 25) hours.

Calculation

To find the value of d, we need more information. Unfortunately, the given information does not provide any additional details about the distance between cities B and C. Therefore, we cannot calculate the exact time it takes for the car to catch up to the truck.

If you have any additional information or if there is anything else I can help you with, please let me know!