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.