I gave the next problem to my students the other day to show them that, if we learn to see our problems in a different new point of view, we may be solving them on a much simpler way.

A lumberjack lives on the side of a river and takes his canoe to go work (somewhere upstream).
On a certain day, when heading to work, he passed through a floating log on the river, exactly one mile away from his house. He proceeded his journey until, after an half of hour he realized he forgot his saw. He immediately turned the canoe around to go pick the saw he left home.
Amazingly, he arrived his house exactly at the same time has the log he saw on the journey up.

Assuming the lumberjack paddled at the same rate in his entire journey, what is the velocity of the stream of the river?

It's possible to solve this on a very simple way. I didn't give any clues to my students, but I will give one to you:

If you read the problem with Einstein eyes, you will solve it in ten earthling seconds.

I'm trying to evaluate the complexity of the problem. Are you capable to solve it in a blink of an eye?

  • $\begingroup$ How can you solve it not in a blink of an eye? The only information given is a time of paddling and the distance the log (i.e. a river) travelled in the time. You can loose arbitrary time before you realize these two values give the result directly – but once you do, you can't in fact do solve the problem in any other way. :) $\endgroup$ – CiaPan Jul 9 at 12:41
  • $\begingroup$ @CiaPan, you could define the velocity of the river $v$ in terms of the velocity of the lumberjack $v_0$. Then, after several calculus steps, you could find $v$ by cancelling $v_0$ (you could never find the lumberjack velocity). You have to do this if you take earth as the referential for the problem. This is not in a blink of an eye... $\endgroup$ – Pspl Jul 9 at 13:37

I think the velocity is

1 mile per hour


Consider the problem in the log's reference frame. In this frame, the velocity of the log is 0, which means the relative velocity of the river is 0 and this means the lumberjack's relative velocity is determined solely by his paddle rate. Since the paddle rate is constant and he turns around half an hour after reaching the log, this means that he reaches the log again in another half an hour, by which point the log has travelled one mile.

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  • $\begingroup$ Bingo! Well done. :) $\endgroup$ – Pspl Jul 9 at 10:51

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