"Impossible" task of Belarusian fifth-graders, which can handle not every adult

  • Dec 24, 2019
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Insidious education system now and then throws "impossible" tasks for solutions, which are often unable to handle the majority of children. Even more interesting is the fact that such problems can not cope in the majority and adults. On one such now and will be discussed.

This task was included in the 5th grade textbook for Belarusian institutions of general secondary education. The same task used in Magnitogorsk in the tournament of young mathematicians among grades 6-8. The task appeared in Barnaul in the competition of 9 classes and on school Olympiad in Nizhny Novgorod for 10 classes.

Condition

We read condition.
We read condition.

On the way past the observer traveled at regular intervals, a bus, a motorcycle and a car. By another observer, vehicles traveled during the same time intervals, but in a different order: bus, car, motorbike. What was the speed of the bus when the vehicle speed - 60 km / h and the motorcycle 30 km / h.

Decision

In fact, everything is simple.
In fact, everything is simple.
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There are several solutions to the problem. Edition Novate.ru lead one of them as an example.
Assume that Vx - is the speed of the bus, you need to find. Let t - is the time spent on the road between the observer vehicle, and - time-interval which drove the bus, car and motorcycle by observers.

Then, the time spent on the road bus between two observers will be t + a, a motorcycle is time t + 2a. Now we can express the distance for each vehicle.

Vehicle: S = 60 ⋅ t
Motorcycle: S = 30 ⋅ (t + 2a)
Bus: S = Vx ⋅ (t + a)

Thus, as the distance for all vehicles was the same, we are the following equation.

car and motorcycle for the distance:

60t = 30 (t + 2a)
60t = 30t + 60a
30t = 60a
a = 0,5t

Car and bus distance:

60t = Vx ⋅ (t + a)
60t = Vx ⋅ (t + 0,5t)
60t = Vx ⋅1,5t
Vx = 60t / 1,5t
Vx = 40

Answer

bus speed was 40 km / h.

I want more interesting things? How about to try 7 puzzles war for the Soviet school, which today does not cope all adults in our time.

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A source:
https://novate.ru/blogs/101218/48717/