1. ## 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.