Question

4) Из пункта А в пункт В выехал велосипедист. Одновременно из пункта В в пункт А навстречу велосипедисту вышел пешеход. После их встречи велосипедист повернул обратно, а пешеход продолжил свой путь. Известно, что велосипедист вернулся в пункт А на 30 минут раньше пешехода, при этом его скорость была в пять раз больше скорости пешехода. Сколько времени затратил пешеход на путь из А в В?

Answer 1

Поскольку скорость велосипедиста в 5  раз больше,  значит и расстояние  до  встречи  больше  в  пять  раз.  Можно  условно  разбить  путь  на  6  частей.  Обратно  велосипедист  проехал  то же  расстояние  5  частей и  пешеход 1  часть.  На  оставшиеся  4  части  пути  он  затратил  30  минут.  Весь  путь  в  1,5  раза  больше  оставшихся  4-х  частей  пути (6/4=1,5).  Значит  время  на  весь  путь  тоже в  1,5 больше.  30*1,5=  45  минут.  Пешеход затратил на путь, только не  из  А в В,  а  из  В  в  А  45  минут.

Answer 2

Problem Analysis

We are given the following information: - A cyclist travels from point A to point B. - At the same time, a pedestrian starts walking from point B towards point A. - After they meet, the cyclist turns back to point A, while the pedestrian continues their journey. - The cyclist returns to point A 30 minutes before the pedestrian. - The cyclist's speed is five times faster than the pedestrian's speed.

We need to determine how much time the pedestrian spent traveling from point A to point B.

Solution

Let's assume the distance between point A and point B is d.

We can use the formula time = distance / speed to calculate the time taken by the cyclist and the pedestrian.

Let's denote the cyclist's speed as v_c and the pedestrian's speed as v_p.

From the given information, we know that the cyclist's speed is five times faster than the pedestrian's speed: v_c = 5 * v_p.

We also know that the cyclist returns to point A 30 minutes before the pedestrian. This means that the time taken by the cyclist is 30 minutes less than the time taken by the pedestrian: time_c = time_p - 30 minutes.

Using the formula time = distance / speed, we can write the following equations:

For the cyclist: time_c = d / v_c.

For the pedestrian: time_p = d / v_p.

Substituting the values of v_c and time_c in terms of v_p and time_p, we get:

d / (5 * v_p) = (d / v_p) - 30 minutes.

Simplifying the equation, we have:

d / (5 * v_p) = d / v_p - 0.5.

Multiplying both sides of the equation by 5 * v_p, we get:

d = 5d - 0.5 * 5 * v_p.

Simplifying further, we have:

0.5 * 5 * v_p = 4d.

Dividing both sides of the equation by 0.5 * 5, we get:

v_p = 0.4d.

Now, we can substitute the value of v_p in terms of d into the equation time_p = d / v_p to find the time taken by the pedestrian:

time_p = d / (0.4d) = 2.5 hours.

Therefore, the pedestrian spent 2.5 hours traveling from point A to point B.

Answer

The pedestrian spent 2.5 hours traveling from point A to point B.