Ants can't walk backwards

Geometry Level 2

An ant starts walking to its nest which is located at distance equal d d . In the first hour, it walked half of the distance. During the second hour, it walked 1 3 \frac{1}{3} of the remaining distance. During the third hour, it walked 1 4 \frac{1}{4} of the remaining distance and so on. After walking for 19 19 hours, the remaining distance becomes 101 101 . Find the value of the original distance d d ?


The answer is 2020.

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Tom You
Jan 19, 2018

d * 1 2 \frac{1}{2} * 2 3 \frac{2}{3} * 3 4 \frac{3}{4} * ... * 19 20 \frac{19}{20} = 101

1 20 \frac{1}{20} d = 101

d = 2020

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