Question 366734
<font face="Garamond" size="+2">


Let *[tex \Large d] represent the distance either up or down the hill (we presume that the hill neither grew nor shrank overnight).  Let *[tex \Large t] represent the time to cover the distance *[tex \Large d] going uphill at *[tex \Large 2.4\text{ kph}].  Then the time for the downhill trip must have been *[tex \Large 11\ -\ t]


Recalling that *[tex \Large d\ =\ rt], describe the uphill trip:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 2.4t]


which can be written:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{d}{2.4}]


Next, describe the downhill trip:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 3.6(11\ -\ t)]


and then solve for *[tex \Large t]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{39.6\ -\ d}{3.6}]


Set the two expressions equal to each other:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{2.4}\ =\ \frac{39.6\ -\ d}{3.6}]


Cross-multiply, collect like terms, and solve for *[tex \Large d]


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>