Question 334623
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Let *[tex \Large d] represent the distance walked.  Then *[tex \Large 5\ -\ d] represents the distance jogged.  Let *[tex \Large t_w] represent the amount of time spent walking and let *[tex \Large t_j] represent the amount of time spent jogging.


In that we know the walking and jogging speeds and the general relationship *[tex \Large t\ =\ \frac{d}{r}] between time, distance, and rate, we can describe the time for each segment of the trip thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t_w\ =\ \frac{d}{4}]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t_j\ =\ \frac{5\ -\ d}{9}]


The total time is the sum of these two times:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ T\ =\ t_w\ +\ t_j]


Substituting to get a function of *[tex \Large d]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ T(d)\ =\ \frac{d}{4}\ +\ \frac{5\ -\ d}{9}]


This needs to be simplified by finding the LCD and adding the two fractions.  I'll leave that part in your capable hands.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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