Question

из пунктов А и В одновременно навстречу друг другу выехал велосипидист и вышел пешеход. Через какое время они встретятся, если велосипедисту на весь путь требуется 40 минут, а пешеходу 2ч?

Answer 1

Problem Analysis

We are given that a cyclist and a pedestrian start simultaneously from points A and B, respectively, and are moving towards each other. We are also given that the cyclist takes 40 minutes to cover the entire distance, while the pedestrian takes 2 hours. We need to determine how long it will take for them to meet.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the cyclist and the pedestrian is the sum of their individual speeds. We can calculate the relative speed and then use it to find the time it takes for them to meet.

Let's denote the distance between points A and B as D. We are given that the cyclist takes 40 minutes (or 40/60 = 2/3 hours) to cover this distance, and the pedestrian takes 2 hours to cover the same distance.

Let's assume the speed of the cyclist is Vc and the speed of the pedestrian is Vp.

We can use the formula: Distance = Speed × Time to relate the distance, speed, and time.

For the cyclist: Distance = Vc × (2/3) hours

For the pedestrian: Distance = Vp × 2 hours

Since the distance covered by both the cyclist and the pedestrian is the same (D), we can equate the two equations:

Vc × (2/3) = Vp × 2

Now, we need to find the time it takes for them to meet. Let's denote this time as T.

The distance covered by the cyclist in time T is Vc × T, and the distance covered by the pedestrian in time T is Vp × T. Since they are moving towards each other, the sum of these distances should be equal to the total distance D:

Vc × T + Vp × T = D

Substituting the value of D from the previous equation, we get:

Vc × T + Vp × T = Vc × (2/3)

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

Calculation

To solve the equation Vc × T + Vp × T = Vc × (2/3), we need to know the values of Vc and Vp. Unfortunately, the given information does not provide these values. Therefore, we cannot calculate the exact time it takes for the cyclist and the pedestrian to meet without additional information.

However, we can still provide a general approach to solving the problem using the concept of relative speed. If we assume some values for Vc and Vp, we can calculate the time it takes for them to meet.

Let's assume Vc = 20 km/h and Vp = 5 km/h. These are arbitrary values for illustration purposes.

Substituting these values into the equation Vc × T + Vp × T = Vc × (2/3), we get:

20 × T + 5 × T = 20 × (2/3)

25 × T = 40

T = 40/25 = 1.6 hours

Therefore, if the cyclist's speed is 20 km/h and the pedestrian's speed is 5 km/h, they will meet after approximately 1.6 hours.

Please note that these values are arbitrary and used for illustration purposes only. The actual values of Vc and Vp are not provided in the given information.

Conclusion

In conclusion, the time it takes for the cyclist and the pedestrian to meet depends on their respective speeds, which are not provided in the given information. However, we can use the concept of relative speed to calculate the time if the speeds are known.