Question

Из города А в город В вышел поезд со скоростью 50км/ч . Через 12 ч из города А вылетел вертолёт , скорость которого в 7 раз больше скорости поезда, и догнал поезд на половине пути от А до В. Найди расстояние между городами.

Answer 1

Problem Analysis

We are given that a train travels from city A to city B at a speed of 50 km/h. After 12 hours, a helicopter takes off from city A and flies at a speed that is 7 times faster than the train. The helicopter catches up to the train when it is halfway between city A and city B. We need to find the distance between the two cities.

Solution

Let's assume the distance between city A and city B is d km.

We know that the train travels at a speed of 50 km/h, so in 12 hours, it covers a distance of 50 * 12 = 600 km.

The helicopter flies at a speed that is 7 times faster than the train, so its speed is 7 * 50 = 350 km/h.

When the helicopter catches up to the train, they have both traveled half the distance between city A and city B. So, the distance covered by the train is d/2 km.

We can set up the following equation to solve for the distance between the two cities:

600 + 350 * t = d/2

where t is the time taken by the helicopter to catch up to the train.

To find t, we can rearrange the equation:

t = (d/2 - 600) / 350

Since the helicopter catches up to the train when it is halfway between city A and city B, the time taken by the helicopter to catch up to the train is also the time taken by the train to travel half the distance between the two cities.

So, we can set up another equation:

t = (d/2) / 50

Setting the two equations equal to each other, we can solve for d:

(d/2 - 600) / 350 = (d/2) / 50

Simplifying the equation:

(d/2 - 600) * 50 = (d/2) * 350

Solving for d:

25d - 30000 = 175d

150d = 30000

d = 200 km

Answer

The distance between city A and city B is 200 km.

Explanation

The train travels at a speed of 50 km/h and covers a distance of 600 km in 12 hours. The helicopter flies at a speed that is 7 times faster than the train, so its speed is 350 km/h. When the helicopter catches up to the train, they have both traveled half the distance between city A and city B. By setting up and solving the equations, we find that the distance between the two cities is 200 km.