SOLUTION: How fast is the river? >> >> A woman boards her canoe and rows upstream away from her dock at a >> steady rate. After two miles, she passes a log floating downriver. >> She k

Question 904768: How fast is the river?
>>
>> A woman boards her canoe and rows upstream away from her dock at a
>> steady rate. After two miles, she passes a log floating downriver.
>> She keeps paddling upstream for an hour, then turns around and rows
>> back downstream.
>> She overtakes the log just as she reaches her dock. How fast is the
>> river flowing?

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Distance where she meets the log = 2miles
speed of current = speed of log =y
let speed of canoe in still water be x
speed upstream = (x-y)
speed downstream = (x+y)

she travels upstream for 1 hour
d=rt
so distance she travels upstream = (x-y)
Time taken to reach starting point
time taken upto the point where she met the log and time taken for 2 miles downstream
= t=d/r
d= (x-y),(x-y), 2
t= 1+((x-y)/(x+y))+2/(x+y) =2/y
1+(2+x-y)/(x+y)=2/y
((x+y)+(2+x-y))/(x+y) =2/y
y(2+2x )=2(x+y)
2y+2xy=2x+2y
2x=2xy
y=1mph the speed of the current
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