** LOGICAL REASONING - SPEED TIME DISTANCE**

** PUZZLE**

Station X of length 900 meters has two station masters A and B. But
as the station is not a busy one, they are mostly jobless and decide to
conduct an experiment. They stand at either end of the station and
decide to note the exact time when trains cross the station masters.
They synchronize their watches and proceed to either end of the station.
Two trains P and Q go past the station (neither train stops here), and
after having taken down their readings, the station masters sit down to
have a chat.

A: Train P entered the station at exactly 8:00:00

B: Train Q entered the station at exactly 8:00:10 (10 seconds past 8)

A: The last carriage of train P crossed me by at 8:00:20, and
precisely two seconds after this, the engines of the two trains went
past each other. (Engines are at the front of the train)

B: The last carriage of train Q crossed me 22 seconds after the engine of P went past me.

A: After the last carriage of train P crossed by me, it took 35 seconds for the engine of train Q to cross me.

B: I got bored and I came here.

#### Questions

- What is the length of train Q?
- At what time do the rear ends of the two trains cross each other?
- How far from station master A do the rear ends of the two trains cross each other?
- You are told that the two trains enter the station at the
same times mentioned and the length of the two trains are unchanged.
Furthermore, train P continues to travel at the same speed (as computed
above). At what minimum speed should train Q travel such that the rear
ends of the two trains cross each other at a point within the length of
the platform?