Question

Из пункта А в пункт В со скоростью 17км/ч выехал велосипедист ,а через 2ч навстречу ему из пункта В со скоростью 6км/ч вышел пешеход .На каком расстоянии от пункта А произошла встреча велосипедиста и пешехода,если известно ,что расстояние между пунктами А иВ равно 103км?

Answer 1

Ко времени выхода пешехода из В велосипедист проехал:
                                                           S₁ = v₁t₁ = 17 * 2 = 34 (км)
Следовательно, расстояние между ними в этот момент было:
                                                           S₂ = S - S₁ = 103 - 34 = 69 (км)
Скорость сближения велосипедиста и пешехода:
                                                             v = v₁ + v₂ = 17 + 6 = 23 (км/ч)

Время до встречи: t = S₂/v = 69 : 23 = 3 (ч)

Велосипедист ехал до встречи: t₂ = t₁ + t = 2 + 3 = 5 (ч)

Расстояние от пункта А до места встречи: S₃ = v₁ * t₂ = 17 * 5 = 85 (км)

Answer 2

Problem Analysis

We are given that a cyclist travels from point A to point B at a speed of 17 km/h, and after 2 hours, a pedestrian starts walking from point B towards point A at a speed of 6 km/h. We need to determine the distance from point A where the cyclist and pedestrian meet, given that the distance between points A and B is 103 km.

Solution

Let's break down the problem step by step:

1. Calculate the distance traveled by the cyclist in 2 hours. 2. Calculate the remaining distance between the cyclist and the pedestrian. 3. Calculate the time it takes for the cyclist and pedestrian to meet. 4. Calculate the distance from point A where the meeting occurs.

Step 1: Distance traveled by the cyclist in 2 hours

The cyclist travels at a speed of 17 km/h for 2 hours. To calculate the distance traveled, we can use the formula:

Distance = Speed × Time

Substituting the values, we get:

Distance = 17 km/h × 2 h

Calculating the distance:

Distance = 34 km.

Step 2: Remaining distance between the cyclist and pedestrian

The total distance between points A and B is given as 103 km. We have already calculated that the cyclist traveled 34 km in 2 hours. To find the remaining distance, we subtract the distance traveled by the cyclist from the total distance:

Remaining Distance = Total Distance - Distance Traveled by Cyclist

Substituting the values, we get:

Remaining Distance = 103 km - 34 km

Calculating the remaining distance:

Remaining Distance = 69 km.

Step 3: Time taken for the cyclist and pedestrian to meet

To find the time taken for the cyclist and pedestrian to meet, we can use the formula:

Time = Distance / Relative Speed

The relative speed is the sum of the speeds of the cyclist and pedestrian. Substituting the values, we get:

Time = Remaining Distance / Relative Speed

Substituting the values, we get:

Time = 69 km / (17 km/h + 6 km/h)

Calculating the time:

Time = 69 km / 23 km/h

Time = 3 hours.

Step 4: Distance from point A where the meeting occurs

To find the distance from point A where the meeting occurs, we can use the formula:

Distance = Speed × Time

Substituting the values, we get:

Distance = 17 km/h × 3 h

Calculating the distance:

Distance = 51 km.

Answer

The meeting between the cyclist and pedestrian occurs at a distance of 51 km from point A.

Conclusion

In this problem, we calculated the distance from point A where the cyclist and pedestrian meet. We found that the meeting occurs at a distance of 51 km from point A.