
Из городов А и В навстречу друг другу одновременно выехали мотоциклист и велосипедист. Мотоциклист
приехал в В на 30 минут раньше, чем велосипедист приехал в А, а встретились они через 10 минут после выезда. Сколько часов затратил на путь из В в А велосипедист?

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Problem Analysis
We have two cities, A and B, and a motorcyclist and a cyclist who start simultaneously from these cities. The motorcyclist arrives in city B 30 minutes before the cyclist arrives in city A. They meet each other 10 minutes after their departure. We need to determine how many hours the cyclist spent on the journey from city B to city A.
Solution
Let's assume that the cyclist's travel time from city B to city A is x hours. Since the motorcyclist arrived in city B 30 minutes before the cyclist arrived in city A, the motorcyclist's travel time from city A to city B is x + 0.5 hours.
We know that they met each other 10 minutes after their departure. This means that the total travel time for both the motorcyclist and the cyclist is x + (x + 0.5) + 0.167 hours (10 minutes is approximately 0.167 hours).
We can set up the following equation to solve for x:
x + (x + 0.5) + 0.167 = x + 0.5
Simplifying the equation:
2x + 0.667 = x + 0.5
x = 0.5 - 0.667
x = -0.167
Since the value of x is negative, it means that the cyclist did not spend any time on the journey from city B to city A. This implies that the cyclist started the journey in city A and arrived in city B.
Therefore, the cyclist did not spend any hours on the journey from city B to city A.
Answer
The cyclist did not spend any hours on the journey from city B to city A.


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