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2025-01-21 18:35:58 -08:00
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\documentclass[
solutions,
singlenumbering,
nopagenumber
]{../../../lib/tex/ormc_handout}
\usepackage{../../../lib/tex/macros}
\title{Warm-Up: Travellers}
\uptitler{\smallurl{}}
\subtitle{Prepared by Mark on \today}
\begin{document}
\maketitle
\problem{}
Four travellers are on a plane, each moving along a straight line at an arbitrary constant speed. \par
No two of their paths are parallel, and no three intersect at the same point. \par
We know that traveller A has met travelers B, C, and D, \par
and that traveller B has met C and D (and A). Show that C and D must also have met. \par
\begin{solution}
When a body travels at a constant speed, its graph with respect to time is a straight line. \par
So, we add time axis in the third dimension, perpendicular to our plane. \par
Naturally, the projection of each of these onto the plane corresponds to a road.
Now, note that two intersecting lines define a plane and use the conditions in the problem to show that no two lines are parallel.
\end{solution}
\end{document}

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[metadata]
title = "Travellers"
[publish]
handout = true
solutions = true