Question

Два тела двигаются навстречу друг другу так, что за каждые 10 секунд расстояние между ними уменьшается на 16 м. Если эти тела будут двигаться в одном направлении с теми же за величиной скоростями, то за 5 секунд расстояние между ними увеличится на 3 м. С какой скоростью двигается каждое из тел?

Answer 1

Сумма скоростей тел 16/10=1,6 м/с
Разность скоростей 3/5=0,6 м/с
Обозначим х-скорость первого тела, у - второго
х+у=1,6
х-у=0,6

х=0,6+у

х+х+0,6=1,6
х=0,5
у=1,1

Вроде бы, так.

Answer 2

Problem Analysis

We are given that two bodies are moving towards each other, and the distance between them decreases by 16 meters every 10 seconds. We are also given that if these bodies move in the same direction with the same speeds, the distance between them increases by 3 meters in 5 seconds. We need to find the speeds of each body.

Solution

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

When the bodies are moving towards each other, the relative speed between them is the sum of their individual speeds. Therefore, the relative speed is v1 + v2.

According to the given information, the distance between the bodies decreases by 16 meters every 10 seconds. This means that in 10 seconds, the relative speed covers a distance of 16 meters. Therefore, we can write the equation:

10(v1 + v2) = 16 When the bodies are moving in the same direction, the relative speed is the difference between their individual speeds. Therefore, the relative speed is v1 - v2.

According to the given information, the distance between the bodies increases by 3 meters in 5 seconds. This means that in 5 seconds, the relative speed covers a distance of 3 meters. Therefore, we can write the equation:

5(v1 - v2) = 3 We now have a system of two equations with two variables. We can solve this system to find the values of v1 and v2.

Solving the System of Equations

Let's solve the system of equations and to find the values of v1 and **v2

Answer 3

Problem Analysis

We are given that two bodies are moving towards each other, and the distance between them decreases by 16 meters every 10 seconds. If these bodies were moving in the same direction with the same speeds, the distance between them would increase by 3 meters in 5 seconds. We need to find the speeds of each body.

Solution

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

We know that when the bodies are moving towards each other, the distance between them decreases by 16 meters every 10 seconds. This can be represented by the equation:

10(v1 + v2) = -16 Similarly, when the bodies are moving in the same direction, the distance between them increases by 3 meters in 5 seconds. This can be represented by the equation:

5(v1 - v2) = 3 We can solve these two equations simultaneously to find the values of v1 and v2.

Solving the Equations

Let's solve the equations using the substitution method.

From equation we can express v1 in terms of v2:

v1 = (-16/10) - v2 Substituting equation into equation we get:

5((-16/10) - v2 - v2) = 3

Simplifying the equation:

-8 - 10v2 = 3

Rearranging the equation:

10v2 = -8 - 3

10v2 = -11

v2 = -11/10

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

v1 = (-16/10) - (-11/10)

v1 = -16/10 + 11/10

v1 = -5/10

Simplifying the fraction:

v1 = -1/2

Answer

Therefore, the first body is moving at a speed of -1/2 units (negative because it is moving towards the second body), and the second body is moving at a speed of -11/10 units (also negative because it is moving towards the first body).

Please note that the units of speed are not specified in the question, so we cannot provide a specific unit for the speeds.

Let me know if you need any further assistance!