Question

Из пункта А в пункт В велосипедист ехал со скоростью 15 км/ч, а возвращался он другой дорогой, длина которой на 10 км длинее, со скоростью 20 км/ч. Обратный путь занял у велосипедиста на 10 минут больше, чем путь из А в В. Найдите длину дороги, по которой велосипедист добрался из В в А. Срочно!!!

Answer 1

Решение в прикреплённом изображении

Answer 2

Problem Analysis

We are given that a cyclist traveled from point A to point B at a speed of 15 km/h and returned from point B to point A on a different road, which is 10 km longer, at a speed of 20 km/h. The return trip took the cyclist 10 minutes longer than the trip from A to B. We need to find the length of the road on which the cyclist traveled from B to A.

Solution

Let's assume the distance from A to B is x km. Since the cyclist traveled at a speed of 15 km/h, the time taken for the trip from A to B is x/15 hours.

The distance from B to A is x + 10 km. Since the cyclist traveled at a speed of 20 km/h, the time taken for the return trip from B to A is (x + 10)/20 hours.

According to the problem, the return trip took the cyclist 10 minutes longer than the trip from A to B. Since 1 hour is equal to 60 minutes, we can convert 10 minutes to hours by dividing by 60: 10/60 = 1/6 hours.

Therefore, we can set up the equation:

(x/15) + (1/6) = (x + 10)/20

To solve this equation, we can multiply both sides by the least common multiple (LCM) of the denominators, which is 30:

30 * (x/15) + 30 * (1/6) = 30 * (x + 10)/20

Simplifying the equation:

2x + 5 = 3(x + 10)

Expanding and simplifying further:

2x + 5 = 3x + 30

Subtracting 2x from both sides:

5 = x + 30

Subtracting 30 from both sides:

-25 = x

Therefore, the distance from A to B is -25 km. However, since distance cannot be negative, we can conclude that there is an error in the problem statement or the given information. Please double-check the problem and provide the correct information.

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