Two hundred fence posts are to be placed into the ground in a straight line, 2m apart. The fence posts are stacked in a pile along this same line, 2 m from the position of the first post to be put in. Maybell is going to put inthe posts one at a time in order, and each post she puts in is farther away from the pile. Maybell can only carry one post at a time, and so she always walks back to the pile to getthe next post. If Maybell starts at the pile, how many kilometers must she walk to finish the job?
+128475
Note that to put in the first post and return, she walks 2 * 2 m = 4m = 4 (1) m
And the total distance she walks to put in the second post is 2 * 4m = 8m = 4 (2) m
And the distance she walks to put in the third post is 2 * 6m = 12m = 4 (3) m
So....to put in N posits...it appears that the total distance waked is
4 ( 1 + 2 + 3 + ......+ N ) m
And the sum of the first positive N integers can be expressed as (N /2) * (N + 1)
So...the total distance she walks (in meters) for 200 posts is :
4 [ (200/2) (201) ] = 2 (200)(201) = 80, 400 m
Converting this to kilometers, she walks 80,400 / 1000 =
80.4 km !!! that's a lot of walking !!!
