A man walks in the same direction as a slowly moving train ($v_{man} > v_{train}$). He counts the train to be 18 steps long. Then he turns around and counts the train to be 11 steps long.
(Suppose both man and train are moving at a constant speed; every step is the same length.)
How long is the train?
For some reason I always end up with two equations and four unknowns... I'd really appreciate a solution!
Key is to notice that your steps provide you with a unit length as well as a unit time. So, let's measure distance in $steps$ and time in $ticks$, with your speed being $1 \ step/tick$.
The length of the train is $x$ steps, and its speed is $v \ steps/tick$ ($v<1$).
It follows that
$$x \ + \ 18 \ v \ = \ 18 $$ $$x \ - \ 11 \ v \ = \ 11 $$
Adding 11 times the first equation to 18 times the second yields $29 x = 396$. The train is $396/29 \ steps$ long.
You also need to check if indeed $v < 1 \ step/tick$. Leave that to you to demonstrate.
