Question

Расстояние между городами касимов и орехов 31 км/ч.из касимова в орехов вышел пешеход со скоростью 5 км/ч.через час оттуда же вышел второй со скоростью 6 км/ч.На каком расстоянии от орехова второй достигнет первого7

Answer 1

Х-время движения второго пешехода до встречи
(х+1)-время движения первого пешехода до встречи, (который вышел на час раньше)
5(х+1)-расстояние, которое пройдет первый пешеход до встречи
6х-расстояние, которое пройдет второй пешеход до встречи
 Но поскольку встреча состоялась, то эти расстояния равны между собой. Запишем уравнение.
5(х+1)=6х
5х+5=6х
5=6х-5х
х=5-время движения.(час)
6*5=30км пройдет второй, а все расстояние между городами 31км.
31-30=1(км)-за один км до Орехова произойдет встреча

Answer 2

Problem Analysis

We are given that the distance between the cities of Kasimov and Orekhov is 31 km. A pedestrian starts walking from Kasimov to Orekhov at a speed of 5 km/h. After an hour, another pedestrian starts walking from the same point to Orekhov at a speed of 6 km/h. We need to determine at what distance from Orekhov the second pedestrian will catch up to the first pedestrian.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the two pedestrians is the difference in their speeds, which is 6 km/h - 5 km/h = 1 km/h.

Let's assume that the second pedestrian catches up to the first pedestrian after t hours. During this time, the first pedestrian would have covered a distance of 5t km, and the second pedestrian would have covered a distance of 6t km.

Since the distance between the two cities is 31 km, we can set up the following equation:

5t + 1t = 31

Simplifying the equation, we get:

6t = 31

Solving for t, we find:

t = 31 / 6

Now, we can calculate the distance from Orekhov where the second pedestrian catches up to the first pedestrian by substituting the value of t into either of the distance equations:

Distance = 6t = 6 * (31 / 6) = 31 km

Therefore, the second pedestrian will catch up to the first pedestrian at a distance of 31 km from Orekhov.

Answer

The second pedestrian will catch up to the first pedestrian at a distance of 31 km from Orekhov.