Question 1126193: M, N, K, and L are marked in a sequence on the straight line. It is known that MN = 13, NK = 11, KL = 14 and LM = 12. What is the distance between the extremes?
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
Think of the points on a number line.
From M to N is 13 units, in one direction or the other, so the change is either +13 or -13.
From N to K is 11 units, in one direction or the other, so the change is either +11 or -11.
From K to L is 14 units, in one direction or the other, so the change is either +14 or -14.
From L to M is 12 units, in one direction or the other, so the change is either +12 or -12.
From M to N to K to L to M gets us back where we started; so the net change must be 0.
That means we need to assign signs to each of the distances so that their sum is 0.
With the given distances, the 13 and 12 must be in one direction and the 14 and 11 in the other.
Then drawing a diagram shows that the distance between the extremes is 25.
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