A sunbather, drifting downstream on a raft, drives off the raft just as it passes under a bridge and swims against the current for 15min. She then turns and swims downstream, making the same total effort and overtaking the raft when it is 1.0km down stream from the bridge. What is the speed of the current in the river?
The Attempt at a Solution
This question is owning me. Hard. I've tried at least 10different methods to crack this but, alas, I figure afterwards that my logic must be wrong, or stuff doesn't cancel out... I'll try to show my work at best I can but most of it is abstract so... Here goes.
Ok so we know that she travels x distance in 15mins opposite to the raft, so her velocity would be.
We also know that in the 15mins the raft travels y distance, and is effectively traveling with the current so,
Now I know that the velocity that the girl is going at is her velocity relative the the ground, so we need to make her velocity relative to the water.
Vgirl.water= Vgirl.ground - Vraft
After around here my logic is hazy and I'm not quite sure how to continue next... Or if even what i'm doing up to this point is correct. Help would be appreciated =)