SOLUTION: 80 coins are placed in a line on the ground. The distance between any two consecutive coins is 10 metres. How far must a person travel to bring them, one by one, to a basket placed

Algebra ->  Finance -> SOLUTION: 80 coins are placed in a line on the ground. The distance between any two consecutive coins is 10 metres. How far must a person travel to bring them, one by one, to a basket placed      Log On


   

Question 1149117: 80 coins are placed in a line on the ground. The distance between any two consecutive coins is 10 metres. How far must a person travel to bring them, one by one, to a basket placed 10 metres behind the first coin.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
80 coins are placed in a line on the ground. The distance between any two consecutive coins is 10 metres. How far must a person travel to bring them, one by one, to a basket placed 10 metres behind the first coin.
-----------
You didn't say where the person started from.
---
If he starts at the basket:
The 1st trip is 20 meters.
The 2nd trip is 40 meters.
---
The last trip is 1600 meters.
The average trip is (1600 + 20)/2 = 810 meters
There are 80 trips
80*810 = 64800 meters

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


1st coin: 10m to the coin and 10m back to the basket = 20m
2nd coin: 20m to the coin and 20m back to the basket = 40m
3rd coin: 30m to the coin and 30m back to the basket = 60m
...
80th coin: 800m to the coin and 800m back to the basket = 1600m

Total distance: (20+40+60+...+1600)m

Use the formula for the sum of an arithmetic sequence:

S+=+n%28%28a1%2Ban%29%2F2%29+=+80%28%2820%2B1600%29%2F2%29+=+80%28810%29+=64800

ANSWER: 64,800 meters