Question

Велосипедист выехал с постоянной скоростью из города А в В, расстояние между которыми равно 100 км. Отдохнув, он отправился обратно в А , увеличив скорость на 15 кмч. По пути он сделал остановку на 6 часов, в результате чего затратил на обратный путь столько же времени, сколько на путь из А в в. Найдите скорость велосипедиста на пути А в В. Помогите, пожалуйста(

Answer 1

Пусть из А в В велосипедист ехал со скоростью х км в час
$\frac{100}{x}$ часов затратил на путь от А до В
 
Из В в А велосипедист ехал со скоростью (х+15) км в час
$\frac{100}{x+15}$ часов затратил на путь от А до В
Составим уравнение
$\frac{10}{x}= \frac{10}{x+15}+6 \\ \\ 10(x+15)=10x+6x(x+15) \\ \\ x^{2} +15x-250=0$
D=225+1000=1225
Корни
10 и (-25)
Ответ. 10 км в час.

Answer 2

Problem Analysis

A cyclist travels from city A to city B at a constant speed. After resting, the cyclist returns from city B to city A at a higher speed. The cyclist takes a 6-hour break during the return journey, which results in the same amount of time spent on the return journey as on the journey from A to B. We need to find the speed of the cyclist on the journey from A to B.

Solution

Let's assume the speed of the cyclist on the journey from A to B is x km/h.

On the journey from A to B, the distance is 100 km, and the speed is x km/h. Therefore, the time taken for this journey is 100/x hours.

On the return journey from B to A, the distance is again 100 km, but the speed is increased by 15 km/h. Therefore, the speed on the return journey is (x + 15) km/h.

During the return journey, the cyclist takes a 6-hour break. This means the time taken for the return journey is the same as the time taken for the journey from A to B, which is 100/x hours.

Using this information, we can set up the following equation:

100/x = 100/(x + 15)

To solve this equation, we can cross-multiply:

100(x + 15) = 100x

Simplifying the equation:

100x + 1500 = 100x

We can see that the variable x cancels out, which means the equation is not solvable. This indicates that there is no unique solution for the speed of the cyclist on the journey from A to B.

Therefore, it is not possible to determine the speed of the cyclist on the journey from A to B based on the given information.