What Is the Speed of the Current in the River?

[Malgrif]

Homework Statement

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?

t= 0.25h
d_r=1.0km

Homework Equations

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.

V_girl.ground= -(x/0.25)

We also know that in the 15mins the raft travels y distance, and is effectively traveling with the current so,

V_raft= y/0.25

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.
V_girl.water= V_girl.ground - V_raft

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 =)

 

[Delphi51]

Sorry, I am old and can't wrap my mind around the particular variables you have used, but I see that you are on the right track. Humor me and think of
u = speed of swimmer with respect to the water
v = speed of water in river
t = time of swim downstream
t + .25 = time raft drifts downstream
d = distance swum upstream

Then write a d = vt equation for the raft, the upstream swim and the downstream swim.
You have unknowns u, v, t and d. And only 3 equations.
1 = v(t + .25) for the raft
d = (u-v)*.25 for swimming upstream

Curious - I find a solution of t = .25, v = 2 with ANY value you like for u.