Question

Пешеход шел из пункта A в пункт B со скоростью 5км/ч.На обратный путь пешеход затратил на 0,4ч меньше,увеличив скорость на 0,5км/ч.Найдите расстояние между пунктами A и B

Answer 1

X/5 - x/5,5=0,4
x/5 - 10x/55=0,4
x/5 -2x/11=0,4
11x-10x=0,4 × 5 × 11
x=22(км)

Answer 2

Problem Analysis

We are given that a pedestrian walks from point A to point B at a speed of 5 km/h. On the return journey, the pedestrian takes 0.4 hours less time and increases their speed by 0.5 km/h. We need to find the distance between points A and B.

Solution

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

On the forward journey, the pedestrian's speed is 5 km/h. Therefore, the time taken to travel from A to B is given by:

Time forward = Distance / Speed = d / 5

On the return journey, the pedestrian's speed is increased by 0.5 km/h, making it 5 + 0.5 = 5.5 km/h. The time taken to travel from B to A is 0.4 hours less than the time taken on the forward journey. Therefore, the time taken on the return journey is:

Time return = Time forward - 0.4

Using the formula for time, we can write:

Time return = Distance / Speed return = d / 5.5

Equating the two expressions for time, we have:

d / 5 = d / 5.5 - 0.4

Simplifying the equation, we get:

d / 5 - d / 5.5 = 0.4

To solve for d, we can multiply both sides of the equation by the least common multiple (LCM) of 5 and 5.5, which is 55:

11d - 10d = 0.4 * 55

d = 0.4 * 55

Therefore, the distance between points A and B is:

d = 22 km

Answer

The distance between points A and B is 22 km.