Question 671841
<font face="Times New Roman" size="+2">


There is no information about the proportions of the trip, either coming or going, that are level, uphill, or downhill.  Does it matter?  If the whole trip were level, then in 1 hour she would travel 9 miles at 9 miles per hour.  But what about the other extreme.  Let's say that the destination is on a continuous upslope from the start.  That means she goes uphill all the way going outbound and downhill all the way going outbound.  Let *[tex \LARGE x] represent the one-way distance.


Distance divided by rate is time, so:


The outbound trip is *[tex \LARGE \frac{x}{6}\ =\ t]


and the return trip is *[tex \LARGE \frac{x}{18}\ =\ 1\ -\ t]


A little algebra music, Sammy:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x}{18}\ -\ 1\ =\ -\ t]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 18}{18}\ =\ -t]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 24t\ =\ 108]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 4.5]


So that is 4.5 miles one direction and 4.5 miles the other direction.  That makes the same 9 miles we got when the terrain was flat.  9 miles total travelled regardless of the terrain.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>