math word problem?

Question

does anyone know how to do this problem plus an explanation on how its done?
two miles upstream from his starting point, a canoeist passed a log floating in the river's current. after paddling upstream for one more hour, he paddled back and reached his starting point just as the log arrived. find the speed of the current.

Answer 1

There is a unique solution for the speed of the current:
Let upstream be positive, and an upstream velocity be positive.
Let C be the velocity of the current, so C is negative.
Let P be the rate of the paddler in still water. P can be either positive or negative depending on which way he's rowing.
Let s be position, and let s = 0 at the instant the paddler passes the log.
Let T be the time it takes the log to go 2 miles downstream.
The canoeist goes upstream at a rate of P + C for 1 hour traveling P+C mi.
Then he goes downstream at a rate of -P + C for T - 1 hours.
Here's the equation:
position of the paddler = position of log = -2 [at time T]
(P + C) + (-P + C)(T - 1) = CT = -2
P + C - PT + P + CT - C = -2
P - PT + P + CT = -2
2P - PT = 0
P(2 - T) = 0
So either P is zero or 2 - T = 0
T = 2
CT = -2
C(2) = -2
C = -1, so the current is 1mi/hr
Oddly enough, as long as C = -1, any value of P faster than the current will satisfy the original equation.

Answer 2

You need some kind of number in there. or time.