<p>The perimeter of the rectangle above is 70 yards. Tom starts at point A and walks 50 yards counterclockwise along the perimeter of the rectangle. At the same time, Alice begins walking from a different point clockwise along the rectangle and continues until she has walked 40 yards. If Tom and Alice end up eight yards apart when they are done walking, what is the greatest distance, in yards, along the perimeter or the rectangle that could have separated them when they started walking?</p>
<p>Does the picture of the rectangle show its dimensions? I just made up a rectangle and got 28, but I don’t know if it’s dependent on the rectangle. </p>
<p>I had a 20x15 rectangle because 20<em>2+15</em>2=40+30=70. I started Tom in the bottom left corner, call it point A, and he walks counterclockwise until he gets to the top right corner, call it point B. He walks there because it’s 15+20+15=50 the way I labeled my sides, which puts him exactly at that corner and at 50 yards. </p>
<p>I assumed that Tom and Alice are eight yards apart along the rectangle, i.e. not cutting through it. Alice is then either eight yards from Tom one way or the other, meaning clockwise or counterclockwise. If you work backwards from one point you find that she would have started 28 yards from him if she went clockwise from her starting point, and if you work backwards from the the other point she would have started 12 yards from him, so at most 28 yards.</p>