The school of over-thinking simple puzzles.

I've stared at this poster while waiting for my train in the morning almost every day for the last three weeks. If you can't see the image, it's a poster for a new programme on Dave (a comedy tv channel) with Dara O Briain called The School of Hard Sums. It has this written on it:

You are waiting for a train.

It is 12:01 exactly. Trains arrive every time the minute hand lies on top of the hour hand.

How long do you have to wait until the next train (If it's on time!)?

I have had the following reactions to this poster, chronologically:

1:05. So a wait of 1 hour 4 minutes.

It's 1:05.

Dara, that isn't even "sums", it's imagining a clock face.

Is this a trick question? Am I missing something?

Ok, fine, it might be slightly after, but I don't think the hour hand would move far enough in five minutes to be significant.

...

Five minutes is 1/12 of an hour; five minutes divided by twelve is 25 seconds.

1:05:25, Dara, that's as precise as I'm willing to get.

Unless you want to count the little bit for however many nanometers the hour hand would move ahead in 25 seconds.

I mean, I don't even know the specifications of this hypothetical clock! Maybe it's one of those ones that ticks over every minute, instead of moving smoothly. And I don't know the width of the hands, either.

You have to give me more details here, Dara.

Dara.

Dara.

Dara.

Just put a new riddle up already.

...

...

... I still don't really want to watch this programme.