Great post but you've made a slight error here, the good thing is that it is really quite easy to spot if you think about it.
You've said that "in 54 minutes you travel (54 * 9) / 10 = 48.6 miles". But we already know that we were travelling with 15mph, so in less then one hour there's now way we can have travelled more than 15 miles.
The correct answer should be that in 54 minutes you travel 13.5 miles (15 miles per hour, and 54 minutes is 9/10 of an hour. So therefore I substracted 1.5 from 15 and got 13.5).
So final answer is 30+13.5=43.5 miles in 2 hours and 54 minutes (notice this is very close to 45 miles that you would travel in 3 hours, so the answer makes sense).
ehehe, you're right, I got the numbers mixed up while writing the post. Well, I've already learned one thing today: never post math stuff here before drinking the morning coffee!
I'm going to edit the post, thanks for spotting the error!