Question

Из города А в город В вышел поезд со скоростью 50 км/ч. Через 12ч из того же города вслед поезду вылетел верталёт, скорость которого в 7 раз больше скорости поезда и догнал поезд на полавине пути от А до В. Опредили расстояние между горадами.

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 the same city and flies towards the train. The speed of the helicopter is 7 times greater than the speed of the train. The helicopter catches up to the train when it is halfway between city A and city B. We need to determine the distance between the two cities.

Solution

Let's assume that 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 would have covered a distance of 50 km/h * 12 h = 600 km.

When the helicopter takes off, it flies towards the train and catches up to it when the train has covered half the distance between city A and city B. Therefore, the train has traveled D/2 km.

The speed of the helicopter is 7 times greater than the speed of the train, so the speed of the helicopter is 7 * 50 km/h = 350 km/h.

Since the helicopter catches up to the train when it has traveled D/2 km, we can calculate the time it takes for the helicopter to cover this distance using the formula:

Time = Distance / Speed

Substituting the values, we get:

D/2 km / 350 km/h = 12 hours

Simplifying the equation, we find:

D = 2 * 350 km/h * 12 hours = 8400 km

Therefore, the distance between city A and city B is 8400 km.

Answer

The distance between city A and city B is 8400 km.