When a train Q vacated station A at 4 am and reached station B at 7 am. Another train P Vacated station B at 6 am and reached station A at 8:30 am. At approximate what time do the two trains crossed each other.

Solution

Let  be the distance between station B and C = d  Then, the Speed of Q = d/ 3  Speed of P = 2d/ 5  Therefore, Relative speed = d /3 + 2d/ 5 = 11d /15  Now, trains meet each other after 6am, when train P starts its journey.  So, distance travelled by Q from 4am to 6am = 2 x d3 = 2d/3 Then, the Remaining distance will be = d – 2d /3 = d /3  Hence there would be time taken to cross each other = d/ 3 /11d /15 = 5/ 11 hr  = 5 /11 x 60 = 27 min( approximately)  Therefore, both of them cross each other at = 6:27 am