One hundred stones are placed on the ground 2 feet apart, the first being 2 feet from a basket. If the basket and all of the stones are in a straight line, how far does a person travel who starts from the basket and brings the stones to it one by one?
2007-12-07 07:06:03 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Total distances are...
2 + 4 + 6 + 8 + ... + 202
Must double that for the return trips...
( 2 ) ( 2 + 4 + 6 + 8 + ... + 202 )
Factor out another two...
4 ( 1 + 2 + 3 + 4 + ... + 100 )
Sum the terms in parenthesis...
4 ( 100 ) ( 100 + 1 ) / 2
Which simplifies to 20,200.
2007-12-07 07:11:03 · answer #1 · answered by jgoulden 7 · 0⤊ 0⤋
To get to the first stone 4 feet.
To the 2nd stone 8 feet
To the 3rd stone 12 feet
etc.
This is just 4(1 + 2 + 3 + 4 + 5 + ... + 100)
The formula for the sum of 1 through 100 is:
(100 x 101) / 2 = 10100 / 2 = 5050
Multiplying by 4 you get:
4 x 5050 = 20,200 feet.
2007-12-07 07:12:22 · answer #2 · answered by Puzzling 7 · 0⤊ 0⤋
http://helpthismother.blogspot.com/
2007-12-07 07:12:49 · answer #3 · answered by Anonymous · 0⤊ 0⤋