Question

Из пункта A в 9 ч. 00 мин. выехал велосипедист и приехал в пункт B в 10 ч. 00 мин. Из пункта B в 9 ч. 00 мин. по той же дороге выехал мотоциклист и приехал в пункт A в 9 ч. 40 мин. Через сколько минут после начала движения они встретились, если оба ехали с постоянной скоростью?

Answer 1

Скорость первого - $V_1=const$
скорость второго - $V_2=const$

затраченное время первым: $\Delta t_1$
затраченное время первым: $\Delta t_2$

$\Delta t_1\ \textgreater \ \Delta t_2$ - по условию,
значит $V_1\ \textless \ V_2$

$L=\Delta S_1=\Delta S_2$ - пройденный путь первым и вторым
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$> В момент встречи они находяться в какой-то точке O, которая на отрезке AB, <img src=$

До момента встречи оба затратили одно и тоже время $\Delta t_{meet}$

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из первых двух уравнений:
$V_1=\frac{L}{\Delta t_1}\\ V_2=\frac{L}{\Delta t_2}$

тогда имеем:
$L=(\frac{L}{\Delta t_1}+\frac{L}{\Delta t_2})*\Delta t_{meet}\\\\\ L*1=L*(\frac{1}{\Delta t_1}+\frac{1}{\Delta t_2})*\Delta t_{meet}\\\\ 1=\frac{\Delta t_1+\Delta t_2}{\Delta t_1*\Delta t_2}*\Delta t_{meet}\\\\ \Delta t_{meet}=\frac{\Delta t_1*\Delta t_2}{\Delta t_1+\Delta t_2}=\frac{40*60}{40+60}\ min=24\ min$

Answer 2

Problem Analysis

We are given that a cyclist left point A at 9:00 AM and arrived at point B at 10:00 AM. Then, a motorcyclist left point B at 9:00 AM and arrived at point A at 9:40 AM. We need to determine how many minutes after the start of their journeys they met, assuming both were traveling at a constant speed.

Solution

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

We know that the cyclist traveled from A to B in 1 hour (60 minutes), and the motorcyclist traveled from B to A in 40 minutes.

To find the speed of each traveler, we can use the formula speed = distance / time.

For the cyclist: - Speed of the cyclist = d / 60 (since the cyclist traveled for 60 minutes)

For the motorcyclist: - Speed of the motorcyclist = d / 40 (since the motorcyclist traveled for 40 minutes)

Since both travelers were traveling at a constant speed, we can set up an equation to find the meeting time. Let's assume the meeting time is t minutes after the start of their journeys.

For the cyclist: - Distance traveled by the cyclist = speed of the cyclist * t = (d / 60) * t

For the motorcyclist: - Distance traveled by the motorcyclist = speed of the motorcyclist * t = (d / 40) * t

Since they met, the sum of the distances traveled by the cyclist and the motorcyclist should be equal to the total distance between points A and B: (d / 60) * t + (d / 40) * t = d

Now, we can solve this equation to find the value of t.

Calculation

Let's solve the equation to find the value of t:

(d / 60) * t + (d / 40) * t = d

Multiplying both sides of the equation by 120 (the least common multiple of 60 and 40) to eliminate the denominators:

2d * t + 3d * t = 120d

5d * t = 120d

Dividing both sides of the equation by 5d:

t = 120 / 5 = 24

Therefore, the two travelers met 24 minutes after the start of their journeys.

Answer

The cyclist and the motorcyclist met 24 minutes after the start of their journeys, assuming both were traveling at a constant speed.