Distance between Points on a Line
Date: 10/02/2002 at 20:15:37 From: CJ Subject: Patterning/Problem solving Five points are located on a line. When the ten distances between pairs of points are listed from smallest to largest, the list reads: 2,4,5,7,8,k,13,15,17,19. What is the value of k? Any help would be greatly appriciated!
Date: 10/02/2002 at 23:19:45 From: Doctor Peterson Subject: Re: Patterning/Problem solving Hi, CJ. Interesting problem! The first thing I see is that the smallest distance is 2 (so none of the points are closer than 2 units apart), and the largest is 19 (so the farthest two points are that far apart). Also, the distances are all whole numbers, so the points can all be taken as integers on a number line. We can starting by calling those points 0 and 19: o--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--o 0 19 Now it occurs to me that if we put any point between these, it will give us two distances whose sum has to be 19. So I look at the given distances to find pairs that add up to 19. These are 2+17 4+15 That gives us a couple of possibilities for where two of the remaining three points are. Either we can play with those possibilities and see which work, or we can look for more facts of this sort that might lead us to the fifth point, such as considering what values of k will pair up with given differences to make 19. I'll leave the rest to you; write back if you need more help, and tell me what you found. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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