Question

Пешеход и велосипедист отправляются из пункта А в пункт В одновременно. В пункте В велосипедист поворачивает обратно и встречает пешехода через 20 мин после начала движения. Не останавливаясь, велосипедист доезжает до пункта А, поворачивает обратно и догоняет пешехода через 10 мин после первой встречи. За какое время пешеход пройдет путь от А до В? Дайте ответ в минутах

Answer 1

Рисуем схему. На ней конечные пункты А и В, место 1й встречи обозначим как С, место 2й встречи-Д. Т.к.пешеход прошёл СД за 10мин, а АС за 20мин, значит 2СД=АС. Пусть СД=х, тогда АС=2х. Тогда за 10мин велосипедист проезжает АС+АС+СД=2х+2х+х=5х. Тогда за 20мин он проезжает 2*5х=10х=АВ+СВ. Известно, что АС=2х, значит АС+АВ+СВ=2х+10х=12х=АВ+АВ, тогда АВ=6х. Т.к х(СД) пешеход проходит за 10мин, то 6х он пройдёт за 60мин, т.о. АВ он пройдёт за 60мин

Answer 2

Calculating the Time for the Pedestrian to Travel from A to B

To calculate the time for the pedestrian to travel from point A to point B, we can use the information provided in the question and the given search results.

1. Initial Movement: - The pedestrian and the cyclist start their journey from point A to point B simultaneously. - The cyclist turns back at point B and meets the pedestrian after 20 minutes from the start of the journey. - This means that the cyclist has traveled for 20 minutes before meeting the pedestrian.

2. Second Encounter: - After the first encounter, the cyclist reaches point A, turns back, and catches up with the pedestrian after 10 minutes from their first encounter. - This implies that the cyclist has traveled for an additional 10 minutes after the first encounter to catch up with the pedestrian.

3. Calculating the Pedestrian's Time: - Let's denote the time taken by the pedestrian to travel from A to B as 't' minutes. - The cyclist's speed is constant, so the time taken by the cyclist to travel from A to B is also 't' minutes. - From the given information, we can set up an equation to solve for 't'.

4. Equation Setup: - Using the equation of motion, where distance = speed × time, we can set up the following equation: - Distance covered by the cyclist in 20 minutes = Distance covered by the pedestrian in t minutes + Distance covered by the cyclist in 10 minutes.

5. Solving for 't': - By solving the equation, we can find the value of 't', which represents the time taken by the pedestrian to travel from A to B.

Let's solve the equation to find the time taken by the pedestrian to travel from A to B.