Will you be able to solve the problem for Belarusian fifth graders?

• Will you be able to solve the problem for Belarusian fifth graders?

Insidious education system now and then throws the "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 object is entered in the workbook grade 5 for the Belarusian establishments 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

On the road traveled by an observer 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.

Resolution

for the problem, there are several solutions. 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 past the bus monitors, car and motorcycle.

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 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)