Question

Из двух городов вышли одновременно в одну и ту же сторону два поезда и встретились через 16 часов. Определить скорости поездов, зная, что сумма их скоростей равна 110 км в час, а расстояние между городами 320 км.

Answer 1

320:16=20 (км/ч) скорость сближения или разность скоростей
(110-20):2=90:2=45 (км/ч) скорость первого
45+20=65 (км/ч) скорость второго
Ответ: скорость первого 45 км/ч, скорость второго поезда 65 км/ч

Answer 2

Problem Analysis

We are given that two trains start simultaneously from two cities and travel towards each other. They meet after 16 hours. We need to determine the speeds of the trains, given that the sum of their speeds is 110 km/h and the distance between the cities is 320 km.

Solution

Let's assume the speed of the first train is x km/h and the speed of the second train is y km/h. We know that the sum of their speeds is 110 km/h, so we can write the equation:

x + y = 110 We also know that the distance between the cities is 320 km. The formula to calculate the distance is:

distance = speed * time

For the first train, the distance traveled is x * 16 km, and for the second train, the distance traveled is y * 16 km. Since they meet after 16 hours, the sum of their distances should be equal to the total distance between the cities:

x * 16 + y * 16 = 320 We now 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

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

From equation we can express x in terms of y:

x = 110 - y

Substituting this value of x into equation we get:

(110 - y) * 16 + y * 16 = 320

Simplifying the equation:

1760 - 16y + 16y = 320

The y terms cancel out, and we are left with:

1760 = 320

This equation is not true, which means there is no solution that satisfies both equations. It seems there might be an error in the given information or calculations.

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