Question 1065804

As a rower passes under a bridge, a bottle of whiskey falls into the water.
Since it's half-full, it floats.
The rower doesn't hear it, and continues downstream.
After 20 minutes, he gets thirsty and looks for the bottle.  
Having sobered some, he figures out that it fell into the water.
He turns around and rows upstream.
He finds the bottle 1 mile from the bridge.
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Find the speed of the current.
<pre>I found this problem quite interesting, and so decided to solve it.

Let speed of boat in still water, and speed of current, be S, and C, respectively
Then average speed going DOWNSTREAM, and UPSTREAM are: S + C, and S – C, respectively
Time bottle (and rower) took to get to MEETUP point = {{{matrix(1,3, D/C, or, 1/C)}}}
Distance he’d traveled before noticing the missing bottle: {{{(20/60)(S + C) = (S + C)/3}}}
Distance he traveled to get back to bottle: {{{(S + C)/3 - 1}}}
Also, distance he traveled to get back to bottle: {{{matrix(1,3, (1/C - 20/60)(S - C), or, (1/C - 1/3)(S - C))}}}
We then get: {{{(S + C)/3 - 1  = (1/C - 1/3)(S - C)}}} 
{{{(S + C)/3 - 1 = S/C - 1 - S/3 + C/3}}}
{{{C(S + C) - 3C = 3S - 3C - CS + C^2}}} -------- Multiplying by LCD, 3C
{{{CS + C^2 - 3C = 3S - 3C - CS + C^2}}} 
{{{C^2 - C^2 + CS - 3C - 3S + 3C + CS = 0}}}
2CS – 3S = 0
S(2C – 3) = S(0)
2C – 3 = 0
2C = 3
C, or speed of current = {{{highlight_green(matrix(1,4, 3/2, or, 1.5, mph))}}}