Question 637106
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If it is 81 miles from home to city, then it is 162 miles round trip (unless someone picked up home and moved it during the trip).  If the average speed for the round trip was 54 mph, then dividing the distance by the rate gives the time of 3 hours for the round trip.  Let *[tex \LARGE t] be the time for the outbound trip at *[tex \LARGE x] mph, then the time for the return trip had to be *[tex \LARGE 3\ -\ t] at *[tex \LARGE y] mph.


Given a constant distance, the outbound trip is then *[tex \LARGE xt\ =\ 81] and the return trip is *[tex \LARGE y(3\ -\ t)\ =\ 81].  Since 81 equals 81, we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y(3\ -\ t)\ =\ xt]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \frac{xt}{3\ -\ t}] 


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