The distance between stations A and B is 120 km. After the train leaving A and B, after 3 hours the second train

The distance between stations A and B is 120 km. After the train leaving A and B, after 3 hours the second train departed in the same direction, the speed of which is 10 km / h more than the speed of the second train. It is known that the first train arrived at station B 2 hours earlier than the second. How many hours will the second train take from A to B?

The second train left 3 hours later and arrived 2 hours later, that is, it was on the way 1 hour less than the first train.

Let the speed of the first train be x km / h, then the speed of the second is x + 10 km / h.

Let us compose the equation according to the condition of the problem:

120 / (x + 10) = 120 / x – 1,

120 / (x + 10) = (120 – x) / x,

120 * x = 120 * x – x² + 1200 – 10 * x,

x² + 10 * x – 1200 = 0.

The discriminant of this equation is:

10² – 4 * 1 * (-1200) = 4900.

Since x can only be a positive number, the problem has a unique solution:

x = (-10 + 70) / 2 = 30 (km / h) – the speed of the second train.

30 + 10 = 40 (km / h) – speed of the second train.

This means that the path from A to B of the second train will take:

120:40 = 3 hours.