Question

Из деревни вышел пешеход, а через 2 ч за ним вдогонку отправился велосипедист. Через какое время после своего выезда велосипедист догонит пешехода, если скорость велосипедиста 10 км/ч, а скорость пешехода - одна вторая скорости велосипедиста?

Answer 1

1)5*2=10(км)- расстояние, которое нужно сократить велосипедисту.
2)10-5=5(км/ч)-разница скоростей
3) 10:5=через 2(ч)-после своего выезда велосепедист догонит пешехода
Ответ : через 2 часа

Answer 2

Problem Analysis

We are given that a pedestrian leaves a village on foot, and after 2 hours, a cyclist starts chasing after the pedestrian. We need to determine how long it will take for the cyclist to catch up to the pedestrian, given that the cyclist's speed is 10 km/h and the pedestrian's speed is half the speed of the cyclist.

Solution

Let's assume the speed of the pedestrian is x km/h. According to the problem, the speed of the cyclist is 10 km/h, and the speed of the pedestrian is half the speed of the cyclist. Therefore, the speed of the pedestrian is 5 km/h.

To find the time it takes for the cyclist to catch up to the pedestrian, we can set up the following equation:

Distance = Speed × Time

The distance traveled by the pedestrian in 2 hours is 2 × x km, and the distance traveled by the cyclist in the same time is 2 × 10 km.

Since the cyclist catches up to the pedestrian when they have traveled the same distance, we can set up the equation:

2 × x = 2 × 10

Simplifying the equation, we get:

x = 10

Therefore, the speed of the pedestrian is 10 km/h.

Now, we can calculate the time it takes for the cyclist to catch up to the pedestrian. Let's denote this time as t.

The distance traveled by the pedestrian in time t is 10 × t km, and the distance traveled by the cyclist in the same time is 10 × t km.

Since the cyclist catches up to the pedestrian when they have traveled the same distance, we can set up the equation:

10 × t = 10 × t

This equation is true for any value of t. Therefore, the time it takes for the cyclist to catch up to the pedestrian is any positive value of t.

In conclusion, the cyclist will catch up to the pedestrian after any positive amount of time.

Answer

The cyclist will catch up to the pedestrian after any positive amount of time.