Puzzler from Car Talk (75 miles to home)

On Car Talk, on 10/21, they gave the following puzzler: You are 75
miles from home, traveling 75 miles/hour. You go one mile, then reduce
your speed to 74 miles/hour, and so on, until you travel the last mile
at 1 mile/hour. How long does it take you to get home? They gave it in
multiple choice form; is it:
a) about 2 hours
b) about 5 hours
c) about 8 hours
d) forever

Well, I'm no dummy; I wrote a little AWK script to calculate 1/75+1/74+...+1
and come up with something like 4.8. So, I figure the answer is b).
But I don't see anything particularly magical here or any computational
shortcut.

Well, on the 10/28 show, they gave the answer, which is "about 5 hours".
But they didn't give any particular theory on the problem, other than
that you can add it up and get the right answer. Then, they said
something about taking the natural log of 75 and adding something called
"Euler's constant" and thereby coming up with something like 4.8.

Of course, they didn't explain any of this, so I turn to the newsgroup.
Is there anything to this?

.

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