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Even though this problem is not a geometry question, it does contain
a tricky spatial relationship, so it's a good one to sketch. In fact,
trying to work this one out in your head is pretty risky. The rope can
be drawn as follows:
Using different markings to indicate the different fractional lengths
is a smart idea. Otherwise, your diagram will be hard to read! Here, the
red "knots" are at 
intervals, the blue "knots" at 
and the green ones at  .
Of course, on test day, you won't have colored markers, so use stars,
dots, slashes, etc. Now if we count from left to right, we see that the
sixth knot is at the 
mark and the seventh knot is at the 
mark. So the distance between them is  .
We use a common denominator of 15, so we get  ,
which equals  .
A problem that would've been almost impossible for most of us to work
out in our heads is made much more do-able through the use of a diagram.
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