# Reader Vs. Writer

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• Jan 13th 2006, 08:29 PM
dud
The Reader Vs. The Writer
This riddle is created by me, and is a hypothetical scenario.
It's fairly hard, at least for those without university maths I recon.
The hard part was constructing the functions,
especially the cubic equation was a good and interesting challenge. :)

The Writer is writing a book, and as soon as one page is done The Reader reads it. And so it goes on.

A clever mathematician has figured out functions to represent the speed at which The Writer writes at and The Reader reads at.

$\displaystyle W(d) = 200(\sin{d})+200$
$\displaystyle d = <0, \infty>$
$\displaystyle W(d) = <0, 400>$
This writer is so commited to this endless book, that he only refrains himself from writing 6 days in a full year.
All other days, he writes. If there is a leap year he takes 29th of February off as well.

$\displaystyle R(h)=\frac{1500}{91}(\frac{1}{3}h^3-\frac{9}{4}h^2+\frac{95}{6})$
$\displaystyle h = <0, 6>$
$\displaystyle R(h) = <0, \frac{25800}{91}>$
This function should be treated as a (non-continuous and)cycling function within the bounds of h as stated above.
In other words, from $\displaystyle h = <0, 1>$ is all the reading the reader does on Monday to Tuesday, and $\displaystyle h = <5, 6>$ is Friday to Saturday.
The Reader reads 6 out of 7 days a week. Sunday isn't a reading day for the reader.

When, if ever, will The Reader catch up with The Writer? If so, at what rate?
If, The Reader will never catch The Writer, how much faster does The Writer write than The Reader read?

Extra points if anyone can figure out additional interesting things about this scenario! :D

If something isn't perfectly clear, please don't hesitate to ask. :)
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