(In reply to the above writeup in the Canoe solutionnode)

That would mean that:

Travelling upstream the woman is doing v mph relative to the stream.
Travelling downstream the woman is doing v mph relative to the stream.

The log is always doing 0 mph relative to the stream.

Therefore, relative to the land:

(Assume the current is flowing at c mph)

Upstream, the woman is doing v - c mph.
Downstream, the woman is doing v + c mph.
The log is always doing c mph relative to the land.

Yet the question stated all the speeds were constant. However, relative to the land, the speeds were most definately not constant.

If you assumed the speeds were constant relative to the land you would get a different answer:

Relative to the land:

Upstream, the woman is doing v mph.
Downstream, the woman is doing v mph.
The log is always doing c mph.

Relative to the river:

Upstream, the woman is doing v + c mph.
Downstream, the woman is doing v - c mph.
The log is always doing 0 mph.

So, if she meets the log at 00:00, and paddles for an hour, she would travel v+c miles away from the log by 01:00. She would then meet the log again once the stream/log reached the dock - i.e. after 1/c hours, travelling at v-c mph.
Therefore, she would have travelled a total of (v + c + v/c - 1 miles, in 1 + 1/c hours, and the log would have travelled 1 mile at c mph.
But, she had an overall displacement of 0m, so:

1/(v + c) * (v + c) + 1 * (v + c) - 1/c(v - c) = 0
1 + v + c - v/c - 1 = 0
v + c - v/c = 0
c/v - 1/c = 0
c/v = 1/c

c2 = v
c = sqrt(v)

I'm not entirely sure, (due to my brain becoming mush), but I don't think its possible to actually find a value for c, but I'm happy to be corrected.

But basically, thanks to everything being relative to something else, the question gives enough information to work out one possible answer, but leaves enough details out to make another answer possible but indeterminate.

If this writeup makes sense, it's a miracle. If this writeup is actually correct... well, there's no point worrying about it, because I'm sure I made a mistake somewhere.