Re: WAS: Squashed egos Now: 400% Longer

["Alan D. Miller" <"Alan D. Miller"@educate.com>]

John Posada asked:

<<Is this correction and explaination accurate?

<snip>

> > 4 months is 400% longer than 4 weeks...4 times
> > longer.
>
> Actually, John, 4 months is 300% longer than 4
> weeks, 3 times longer, or 4 times as long.
>
> Assuming 1 month equals 4 weeks:
>  *  One month is 0% longer than 4 weeks (1 time as
> long).
>  *  Two months is 100% longer than 4 weeks (2 times
> as long).
>  *  Three months is 200% longer than 4 weeks (3
> times as long).
>  *  Four months is 300% longer than 4 weeks (4 times
> as long).>>


You are correct, John. Here's why:



If you assume 1 month equals 4 weeks (it doesn't, it's actually 52/12 weeks or
4.333... weeks, but who's counting?), then 4 months equals 16 weeks. Writing
this as a percentage gives us 4 times x times 100% = 16; where x represents the
unknown ratio (percentage), and the 100% is there to convert from a decimal
fraction to percent. Solving for x, we find x = 16/(4 times 100%), or 400%.



The confusion comes with the term "longer than," which may have been an
ill-advised choice here. Your critic seems to have interpreted "longer than" to
mean the difference between 4 weeks and 4 months (16 weeks minus 4 weeks, or 12
weeks) is what the 400% referred to. If you use "as long as", the result is
unambiguously 400%.



Al Miller

alan -dot- miller -at- educate -dot- com