A boat takes 38 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?

Velocity of the stream = 4 km/hr.
The speed of the boat in still water is 14 km/hr.
Speed downstream = 14 + 4 = 18 km/hr.
Speed upstream = 10 km/hr.
Let the distance between A and B be x km.
Time taken to travel downstream from A to B + Time taken to travel upstream from B to C(mid of A and B)
= 38 hours.
⇒ x/18 + (x/2)/10 = 38
⇒ x/18 + x/20 = 38
⇒ 19x/180 = 38
⇒ x/180 = 2
⇒ x = 360 km.