If 25000 people board a ship at a rate of 400 per hour for 10 hours a 37 minutes a day. How long will it take for them to all board the ship?

Do you mean 10 hours AND 37 minutes of boarding per day?

10 h 37 min is 10.2703 h.
In one day, 4108 people are loaded.
After 6 days, 24,648 are loaded.

That leaves 352 more to be loaded.
That will take 0.88 hours of the seventh day. (53 minutes)

Remind me not to go on the cruise ship.