Faceted Curriculum Project/RWP1

Problem Text
"Runway Edge Lights" are placed on either side of a runway, in order for planes to see the edges of a landing strip from far away. These lights should be placed along the edges of 800 meters of the runway, with 50 meters between each light and the next, as displayed below. What is the maximum number of runway edge lights that can be placed along the runway?



Problem Discussion
This problem does not involve intricate algebraic or geometric formulae. However, there are a two subtleties which make it difficult. If the problem is not completely understood, one might simply divide 800 by 50, to obtain an answer: 16 lights. However, it is important to note the following two facts:
 * 1) There should be lights on both sides of the runway.
 * 2) 17 lights can fit along each side of the runway, not 16.

To see the previous fact, it is useful to consider a shorter runway first (using the "Solve a simpler problem" strategy). Suppose for the moment that the runway is only 100 meters long. It is possible to place a runway light at the three positions along the runway -- at 0 meters, 50 meters, and 100 meters -- while keeping them spaced at 50 meter intervals. The division process $$ 100 \div 50 $$ yields an answer of 2, which is one less than the number of runway lights.

Once this is understood, it can be seen that there can be 17 lights on each side, since $$17 = (800 \div 50) + 1 $$.

Doubling 17 yields a total of 34 lights along the runway. It is possible to place 34 lights along the runway, while following the guidelines of the problem.