The train runs the entire distance from A to B according to the schedule in 9 hours.

The train runs the entire distance from A to B according to the schedule in 9 hours. Returning back, for the first 6 hours it walked at the same speed, then reduced the speed by 10 km / h, and therefore arrived at point A with a delay of 30 minutes. Find the initial speed of the train.

Suppose that according to the schedule, the train goes from A to B at a speed of x km / h.

Since the train spent 9 hours on this route, the distance from A to B is 9 * x km.

According to the problem, the return journey for the train took 30 minutes more, which means it took 9.5 hours on the way.

The train went at the same speed for 6 hours, which means it covered a distance of 6 * x km, and the rest of the time (9.5 – 6) = 3.5 hours, it went at a speed of x – 10 km / h. Let’s compose and solve the equation:

9 * x = 6 * x + 3.5 * (x – 10),

9 * x = 6 * x + 3.5 * x – 35,

9.5 * x – 9 * x = 35,

0.5 * x = 35,

x = 70 (km / h) – train speed according to the schedule.