Question

Из пункта A в пункт B велосипедист ехал со скоростью 15 км/ч, а возвращался он другой дорогой,длина которой на 10 км длиннее , со скоростью 20 км/ч.Обратный путь занял у велосипедиста на 10 минут больше , чем путь из A в B. Найдите длину дороги , по которой велосипедист добирался из B в A

Answer 1

30 км/ч дипломат лщорла

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 journey took the cyclist 10 minutes longer than the journey from A to B. We need to find the length of the road the cyclist traveled from B to A.

Solution

Let's assume the distance from A to B is x km. Therefore, the distance from B to A is x + 10 km.

To find the time taken for the journey from A to B, we can use the formula:

Time = Distance / Speed

The time taken for the journey from A to B is given by:

Time(A to B) = x / 15 Similarly, the time taken for the journey from B to A is given by:

Time(B to A) = (x + 10) / 20 We are given that the return journey took the cyclist 10 minutes longer than the journey from A to B. Since 10 minutes is equal to 1/6 of an hour, we can write the equation:

Time(B to A) = Time(A to B) + 1/6

Substituting the values of the time taken for the journeys, we get:

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

To solve this equation, we can multiply both sides by the least common multiple (LCM) of 15 and 20, which is 60:

60 * [(x + 10) / 20] = 60 * [x / 15 + 1/6]

Simplifying the equation:

3(x + 10) = 4x + 10

Solving for x:

3x + 30 = 4x + 10

x = 20

Therefore, the distance from A to B is 20 km, and the distance from B to A is 20 + 10 = 30 km.

Answer

The length of the road the cyclist traveled from B to A is 30 km.