From 7ec80b79ebf301a45331015470984e30e6943060 Mon Sep 17 00:00:00 2001
From: Mark <mark@betalupi.com>
Date: Sun, 14 Jan 2024 19:08:51 -0800
Subject: [PATCH] Added a warm-up

---
 Misc/Warm-Ups/travellers.tex | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100755 Misc/Warm-Ups/travellers.tex

diff --git a/Misc/Warm-Ups/travellers.tex b/Misc/Warm-Ups/travellers.tex
new file mode 100755
index 0000000..0de4c7e
--- /dev/null
+++ b/Misc/Warm-Ups/travellers.tex
@@ -0,0 +1,29 @@
+\documentclass[
+	solutions,
+	singlenumbering,
+	nopagenumber
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+
+\title{Warm-Up: Travellers}
+\subtitle{Prepared by \githref{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}
\ No newline at end of file