CS 2104 Problem Solving in Computer Science           Mini-writing Assignment 3
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This is a purely individual assignment.  Solve the given problem.  Write your 
solution in this file, and explain carefully and clearly how you arrived at
your solution. Turn your solution in by the specified due date.  Submit only 
plain text files for this assignment!
	
Remember that the evaluation of your submission will depend primarily on the 
completeness and clarity of your explanation.
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The Problem:

A driver crossing Kansas travels 50 miles in M minutes.  The driver then switches 
to I-70 and increases his speed by 25%.  In terms of M, how long will it take for
the driver to travel another 50 miles at his increased speed?

Answer:



Explanation:

Recall that the distance traveled is equal to the speed of travel multiplied by
the length of time spent traveling:  distance = rate * time.


A more complex, but perhaps more obvious, analysis:

Now, we know the driver will travel 50 miles at a speed of 1.25*S miles per hour,
where S is the original speed at which the driver was moving.  So, since we can
trivially solve the equation above for time, we see that the time will equal 
(50 miles) / (1.25 S miles per hour) or 40/S hours.

But we need to express this in terms of M.  Since we know the driver traveled 50
miles in M minutes at his original speed, we know that 50 = S * (M/60) and so
S = 3000 / M.

Substituting, we get that the time to travel 40 miles at the increased speed will
be 40 / (3000 / M) or M/75 hours.

Since the original time was M/60 hours, this is 4/5 or 80% of the original time.

So, increasing the speed by 25% reduces the travel time by 20%.


A simpler analysis:

We know that OriginalDistance = OriginalRate*OriginalTime, and we know that
NewDistance = NewRate*NewTime.  But we also know that the distance is the same
in both cases.  (The fact the distance is 50 miles is entirely irrelevant).

We also know that NewRate = 1.25*OriginalRate.

So, we have that OriginalRate*OriginalTime = 1.25*OriginalRate*NewTime, and
so OriginalTime = 1.25*NewTime and therefore NewTime = OriginalTime/1.25.

More simply put, Newtime = 0.80*OriginalTime.