A man rowing upstream drops his hat at point M. Thirty minutes later at N, he notices its loss and rows back. He picks up his hat at P, 440 yards below M. Find the rate of the stream and the total elapsed time.

Answer 1

c = speed of current
r = rowing speed
The time taken by the hat is 440/c minutes
The the rower goes upstream a distance of 30(r-c)
then back that same distance at speed r+c
So we have
440/c = 30 + 30(r-c)/(r+c) + 440/(r+c)
Oddly enough, if the current flows at 22/3 yd/min
then the rower can have any speed greater than that.
For example, if r=44/3, then a total of 60 minutes is used.
But you can plug in other rowing speeds as well.