How the moon is making the days longer

I was talking the other day with a friend, he was telling me that his biological day cycle is approximately 25hrs long as opposed to 24.

It was the 2nd person that was telling me something like that. I argued a bit with him that night-shifting is probably the result

of eager left-brain wanting to steal more of the night and lazy right-brain wanting to sleep longer in the morning - which results in people going later and later to bed when left in their own devices.

Still my friend was convinced that his clock is actually slower - and it is not the result of what I was explaining so jokingly I told him that he is then the man of the future - he just needs to wait for a bit longer for the earth to reach that period, just like the moon, locked facing us in the same way. He looked at me puzzled and at that point we said goodbye.

The long drive after that is an interesting opportunity for me.

I have 40 minutes, unable to use laptop, internet phone, armed exclusively with logic, memorized facts and various brain tools. 

And I have problem to solve. I am not that different from a post-apocalyptic survivor or someone that landed on a new terra but without any of the equipment. 

So the problem at hand: explain how the moon affected and will affect the earth. Prove any points you make.

1. Memory: the moon was something that came from elsewhere and was captured by the gravitational field of the earth.

2. Observation : The moon always looks the same when lighted up - shows always the same face towards the earth.

3. Memory : Geosynchronous satellites are close enough to earth that allow for communication use

4. Memory : Sending a photo-beam to the moon and getting it back here takes more than a second

5. 1 => the moon is smaller than the earth 

6. 3,4 => the moon is turning around the planet much slower than the planet's own rotation 

7. Memory : No rocky planet is perfectly spherical or perfectly homogeneous.

8. Intuition : Due to the quadratic drop by distance of the gravitational field, a round ball turning around an egg shaped ball, laying flat but with an axis on it center will be pulling stronger the closer part than the further part of the elipsis - as a result it will attempt to pull it so as it aligned with it. It is a matter of time for the ellipsis to start rotating locked with the ball around it. If the ball that turns around the other is  also an egg turning around itself it will also eventually be locked in. In the process the turning ball will be slowed down so as the total rotational momentum of the system will remain constant.

Q: The earth isn't egg shaped.

A: No but it is covered with water. Even though the cover is extremely thin (less than paper thin if earth was an orange) the gravitational pull is shaping the water so as the earth's shape is more like an egg

Q: Water around the earth may be adding an egg-shaped skin but its not hard - it fluidly follows the moon. Isn't that different that the egg example above?

A: Yes it is different. Probably it is more intuitive to think of the tidal move of the water as a wave that keeps its crest toward the moon going around the dart. The wave isn't really circulating the water mass but it should be causing a continuous friction similar to that of a rolling ball on  a surface (the static friction that gives the torque to turn the ball is equivalent to the opposite force (and thus tork towards the surface).

Q: Can we calculate how much was the earth's period before the moon?

A: We know the rotational momentum of the system and the ratio of the masses . We don't know what was the original rotation of the moon around the earth (its now 28 days). We know the rotational speed of both moon (28 days - from (2) ) and the earth (1 day). We don't know the moon's initial rotational speed, neither do we know when it reached its stable point. So overall I don't think we can deduce from the above the earth period before the moon arrival. Given however the huge difference (1 vs 28) of the two periods we can estimate that during the past 4B yrs the earth has been decelerating uniformly (slows down by the same amount (absolute or proportional?) every billion years.