Two trains left the two cities at the same time in the same direction and met after 16 hours

Two trains left the two cities at the same time in the same direction and met after 16 hours. Determine the speed of trains, knowing that the sum of their speeds is 110 km per hour, and the distance between cities is 320 km.

Let’s denote the speed of a faster train through x1, and the speed of another train through x2.

Since these trains go in the same direction, the speed at which the distance between these trains decreases is x1 – x2.

According to the condition of the problem, the initial distance between the trains was 320 km, and the trains met after 16 hours, therefore, the following relationship holds:

(x1 – x2) * 16 = 320.

It is also known that the sum of the speeds of these trains is 110 km / h, therefore, the following relationship takes place:

x1 + x2 = 110.

We solve the resulting system of equations. Substituting into the first equation the value x1 = 110 – x2 from the second equation, we get:

(110 – x2 – x2) * 16 = 320;

(110 – 2×2) * 16 = 320;

110 – 2×2 = 320/16;

110 – 2×2 = 20;

2×2 = 110 – 20;

2×2 = 90;

x2 = 90/2;

x2 = 45.

Find x1:

x1 = 110 – x2 = 110 – 45 = 65.

Answer: the speed of one train is 65 km / h, the speed of the other train is 45 km / h.