Question

Из Двух городов, расстояние меду Которыми 560 км, два автомобиля выехали навстречу друг другу и встретились через 4 часа. Если скорость первого автомобиля уменьшить на 15%, а скорость второго увеличить на 20%, то встреча произойдет также через 4 часа. Найдите скорость каждого автомобиля.​

Answer 1

Ответ:

1 - 80 (км/ч)
2 - 60 (км/ч)

Объяснение:

Примем за 100% или за 1 скорость первого автомобиля, тогда можно найти какую часть составляет скорость второго автомобиля от скорости 1.

1) 560:4=140 (км/ч) - скорость сближения.

2) 0,15:0,2 (часть) – составляет скорость второго от скорости первого.

3)  1+0,75 = 1,75 (часть) - приходится на скорость сближения.

4)  140:1,75 = 80 (км/ч) - скорость первого автомобиля.

5)  140-80=60 (км/ч) - скорость второго автомобиля.

Answer 2

Problem Analysis

We are given that two cars start from two different cities and travel towards each other. The distance between the cities is 560 km. The cars meet after 4 hours. If the speed of the first car is reduced by 15% and the speed of the second car is increased by 20%, they will meet again after 4 hours. We need to find the speed of each car.

Solution

Let's assume the initial speed of the first car is x km/h and the initial speed of the second car is y km/h.

According to the given information, the cars meet after 4 hours. The total distance traveled by both cars is equal to the sum of their speeds multiplied by the time taken. Therefore, we can write the equation:

4(x + y) = 560 Now, we are told that if the speed of the first car is reduced by 15% and the speed of the second car is increased by 20%, they will meet again after 4 hours.

Let's calculate the new speeds of the cars: - The speed of the first car after reducing it by 15% is 0.85x km/h. - The speed of the second car after increasing it by 20% is 1.2y km/h.

According to the given information, the cars meet again after 4 hours. Using the same logic as before, we can write the equation:

4(0.85x + 1.2y) = 560 Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From equation we have: 4(x + y) = 560

Simplifying, we get: x + y = 140 Now, let's substitute this value of x + y into the second equation:

4(0.85x + 1.2y) = 560

Simplifying, we get: 3.4x + 4.8y = 560 Now we have a new equation: x + y = 140 3.4x + 4.8y = 560 We can solve this system of equations using any method, such as substitution or elimination. Let's use the elimination method.

Multiplying the first equation by 4.8, we get: 4.8x + 4.8y = 672 Subtracting this equation from the second equation, we eliminate y: (3.4x + 4.8y) - (4.8x + 4.8y) = 560 - 672

Simplifying, we get: -1.4x = -112

Dividing both sides by -1.4, we find: x = 80

Substituting this value of x into the first equation, we can find y: 80 + y = 140

Simplifying, we get: y = 60

Therefore, the initial speed of the first car is 80 km/h and the initial speed of the second car is 60 km/h.

Answer

The speed of the first car is 80 km/h and the speed of the second car is 60 km/h.