Question 326529
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The distance to work is the same as the distance coming home, so for the trip to work:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t_1\ =\ \frac{d}{30}]


and for the trip home


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t_2\ =\ \frac{d}{50}]


The average round trip speed is then 2 times the one-way distance divided by the sum of the elapsed times:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r_{avg}\ =\ \frac{2d}{t_1\ +\ t_2}]


Substituting from the first two relationships:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r_{avg}\ =\ \frac{2d}{\left(\frac{d}{30}\right)\ +\ \left(\frac{d}{50}\right)}]


A little algebra to simplify the compound fraction:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r_{avg}\ =\ \frac{3000}{80}]


Verification of the previous step left as an exercise for the student.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r_{avg}\ =\ 37.5\ mph]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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