A bus departed from point M to point N. Half an hour later, a passenger car left N to

A bus departed from point M to point N. Half an hour later, a passenger car left N to M at a speed exceeding the speed of the bus by 18 km / h. In 1 hour and 20 minutes after leaving, he met a bus, and traveled a distance 3 km more than the bus. What is the distance between M and N?

Let the speed of the bus be x km / h, then the speed of the car is x + 18 km / h.

The bus traveled for 0.5 h and 1 h 20 min in total 1 h 50 min 1 5/6 h and traveled 1 5/6 x km. The car traveled in 1 h 20 min = 1 1/3 h 1 1/3 (x + 18) km, which is 3 km more than the bus:

1 1/3 (x + 18) – 1 5/6 x = 3.

Where,

4/3 x + 24 – 11/6 x = 3 or

8/6 x – 11/6 x = (3 – 24) * 6/6;

8 x – 11 x = – 126 and

x = 41 (km / h) – bus speed;

41 + 18 = 59 (km / h) – vehicle speed.

The distance between M and N is 4/3 * 59 + 11/6 * 41 = 153.3 km.