Tuesday, August 14, 2012

The Final Unicorn Solution

The task is to fill a basin with water.  We know not the volume of this basin...nor do we need to.  We shall merely consider this the job that needs doing.  In fact we shall, upon completion consider this ONE job done.  And we shall use this consideration to build our equation.

First and foremost, this is a work problem, akin to where two or more individuals are working together to perform a task, when we know how long the task will take for each of them individually.

Let's reiterate the facts, shall we?

We have a unicorn fountain statue spewing copious amounts of water from various orifices: eyes, horn, and mouth.

Mouth - takes 6 hours (ancient greek hours) to fill the basin.

Horn - 4 days or 48 hours

Right Eye - 3 days or 36 hours

Left Eye - 2 days or 24 hours

Let X be the amount of time it takes all four orifices to fill the basin.  Let's consider each orifice's contribution toward the completion of this one job.

Mouth:  X/6 because the mouth alone would complete the task in 6 hours

Horn: X/48           Right Eye: X/36         Left Eye:  X/24

Gathered together they each perform the filling of the basin.  In other words, the equation:

X/6  +  X/24  +  X/36  +  X/48  =  1

Solve for X

Multiply by the Common Denominator 144

6X + 4X +  3X + 24X = 144

37X = 144

X = 3.891 to 3 decimal places.

Remember, these are ancient Greek hours and twice as long as present day hours.  Soooooo, in today's parlance about 7.8 Hours.  Roughly about a normal 9 to 5 workday (minus lunch).

Hopefully, you found this as much fun as I did.

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