Tired legs

Calculus Level 1

Frederick begins to walk a distance of $100\text{ m}.$ But he is so tired that, in the first minute, he covers $50\text{ m}.$ In the next minute, he covers half of the remaining distance, i.e. $25\text{ m}.$ Again, in the next minute, he covers half of the remaining distance, which $12.5\text{ m},$ and so on.

Will Frederick be able to complete the $100\text{ m}?$

Yes, between 30 and 60 minutes Yes, between the first and second hour Yes, within 15 minutes No

2 solutions

Bharadwaj Vemparala
Dec 28, 2017

The distance Fredrick covers each minute is a geometric series given by:

$50, 25, 12.5,...$ $\implies$ $50\times (1, \frac{1}{2}, \frac{1}{4},...)$

The sum of the series $1, \frac{1}{2}, \frac{1}{4},...$ to $n$ terms is $2(1-(\frac{1}{2^n}))$ .

For Fredrick to cover $100$ $m$ , the series sum should converge to $2$ . But this happens only when $n\rightarrow\infty$ . Hence Fredrick can never cover the distance!

Actually $87.5m$ at third position...

Kelvin Hong - 3 years, 5 months ago

Raven Herd
Jan 17, 2018

Sum of an infinite gp

Tired legs

2 solutions

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