Question

Из двух поселков, расстояние между которыми равно 38 км, вышли одновременно навстречу друг другу два путешественника. Через 2 часа после выхода им оставалось пройти до встречи еще 20 км. С какой скоростью шел каждый из путешественников, если один из них проходил в час на 1 км больше, чем другой? Системой решить надо(x и y)!

Answer 1

Ответ:

x=4, y=5

Пошаговое объяснение:

за 2 часа оба прошли 38-20=18км, т. е. x+y=18/2, где x y-скорости

тогда система:

x+y=9; x+1=y

подставляем

x+(x+1)=9

2x=8

x=4

y=4+1=5

между x и y нет разницы, может быть и y+1=x, я выбрал так

Answer 2

Problem Analysis

We have two travelers who start simultaneously from two villages that are 38 km apart. After 2 hours, they have 20 km left to reach each other. One traveler walks 1 km per hour faster than the other. We need to find the speeds of both travelers.

Solution

Let's assume the speed of the slower traveler is x km/h. Then the speed of the faster traveler will be x + 1 km/h, as they walk 1 km/h faster.

To solve this problem, we can use the formula: speed = distance / time.

Let's calculate the time it took for each traveler to cover the initial distance of 38 km:

- The slower traveler took 38 / x hours. - The faster traveler took 38 / (x + 1) hours.

According to the problem, after 2 hours, both travelers had 20 km left to reach each other. We can calculate the time it took for each traveler to cover the remaining distance of 20 km:

- The slower traveler took 20 / x hours. - The faster traveler took 20 / (x + 1) hours.

Since both travelers started at the same time, the total time for both of them is the same. We can set up the following equation:

38 / x + 20 / x = 2 + 20 / (x + 1)

Now, let's solve this equation to find the value of x.

Solving the Equation

To solve the equation, we can multiply both sides by x(x + 1) to eliminate the denominators:

38(x + 1) + 20x = 2x(x + 1) + 20x

Expanding and simplifying the equation:

38x + 38 + 20x = 2x^2 + 2x + 20x

58x + 38 = 2x^2 + 22x

Rearranging the equation:

2x^2 + 22x - 58x - 38 = 0

2x^2 - 36x - 38 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values of a, b, and c are:

a = 2 b = -36 c = -38

Substituting these values into the quadratic formula:

x = (-(-36) ± √((-36)^2 - 4 * 2 * (-38))) / (2 * 2)

Simplifying:

x = (36 ± √(1296 + 304)) / 4

x = (36 ± √1600) / 4

x = (36 ± 40) / 4

Now, we have two possible values for x:

1. x = (36 + 40) / 4 = 76 / 4 = 19 2. x = (36 - 40) / 4 = -4 / 4 = -1

Since the speed cannot be negative, we discard the second solution.

Therefore, the speed of the slower traveler is 19 km/h, and the speed of the faster traveler is 20 km/h.

Answer

The slower traveler walked at a speed of 19 km/h, while the faster traveler walked at a speed of 20 km/h.