Question

из вершины прямого угла по его сторонам начинают одновременно двигаться два тела.Через 15 секунд расстояние между ними стало равно 3метра.С какой скоростью двигалось каждое тело, если известно, что первое прошло за 6 секунд такое же расстояние, какое второе прошло за 8 секунд?

Answer 1

1 тело прошло за 6 сек такое же расстояние, как 2 тело за 8 сек.
Значит, 1 тело двигалось быстрее.
Отношение катетов равно 8:6 = 4:3, а гипотенуза равна 3 м.
(4a)^2 + (3a)^2 = 3^2
16a^2 + 9a^2 = 25a^2 = 3
a^2 = 3/25; a = 3/√5 = 3√5/5
За 15 сек 1 тело прошло 4a = 12√5/5, скорость v1 = 12√5/(5*15) = 4√5/25
2 тело прошло за 15 сек 3a = 9√5/5, скорость v2 = 9√5/(5*15) = 3√5/25

Answer 2

Problem Analysis

We have two bodies moving simultaneously from the vertex of a right angle along its sides. After 15 seconds, the distance between them is 3 meters. We need to find the speed at which each body is moving, given that the first body covers the same distance in 6 seconds as the second body covers in 8 seconds.

Solution

Let's assume that the speed of the first body is v1 and the speed of the second body is v2.

We know that distance = speed × time. Therefore, the distance covered by the first body in 6 seconds is 6v1, and the distance covered by the second body in 8 seconds is 8v2.

According to the problem, after 15 seconds, the distance between the two bodies is 3 meters. This means that the sum of the distances covered by the two bodies is equal to 3 meters:

6v1 + 8v2 = 3 We also know that the distance between the two bodies is equal to the difference between the distances covered by the two bodies:

8v2 - 6v1 = 3 Now we have a system of two equations with two variables. We can solve this system to find the values of v1 and v2.

To solve the system, we can use the method of substitution or elimination. Let's use the method of elimination.

Multiplying equation by 8 and equation by 6, we get:

48v1 + 64v2 = 24 48v1 - 36v2 = 18 Subtracting equation from equation we eliminate v1:

100v2 = 6 Dividing both sides of equation by 100, we find:

v2 = 0.06 m/s

Substituting the value of v2 into equation we can find v1:

8(0.06) - 6v1 = 3

0.48 - 6v1 = 3

-6v1 = 2.52

Dividing both sides of the equation by -6, we find:

v1 = -0.42 m/s

Since speed cannot be negative, we discard the negative value of v1. Therefore, the speed of the first body is 0.42 m/s and the speed of the second body is 0.06 m/s.

Answer

The first body is moving at a speed of 0.42 m/s and the second body is moving at a speed of 0.06 m/s.

Explanation

The problem can be solved by setting up a system of equations based on the given information. By solving the system, we find that the first body is moving at a speed of 0.42 m/s and the second body is moving at a speed of 0.06 m/s.