A train starts from A at 6 AM and reaches B at 11 AM on the same day. Another train starts from B at 8 AM and reaches A at 3 PM on the same day. At what time the two trains will have crossed each other?

Let's assume the distance between A and B is 35 km.

A train starts from A at 6 AM and reaches B at 11 AM on the same day.

Total time taken by first train = 5 hours

Speed of first train = $$\frac{35}{5}$$

= 7 km/h

Another train starts from B at 8 AM and reaches A at 3 PM on the same day.

Total time taken by second train = 7 hours

Speed of second train = $$\frac{35}{7}$$

= 5 km/h

As given in the question, first train start at 6 AM and second train started at 8 AM. It means that first train started 2 hours before the second train.

Distance covered by the first train in 2 hours = $$7\times2$$ = 14 km

Remaining distance = 35-14 =  21 km

So the remaining distance will be covered by both of the trains together to cross each other.

Time taken by both of them toegther to cross each other = $$\frac{21}{7+5}$$

= $$\frac{21}{12}$$

= $$\frac{7}{4}$$

= $$1\frac{3}{4}$$

=  1 hour 45 minutes

So after 8 AM, both trains will run 1 hour 45 minutes more to cross each other.

Hence the time will be 9:45 AM.