Question 182256
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Let the time to travel to the retreat be <i>t</i> hours, then the time to return from the retreat must be 10 - <i>t</i>.


Knowing that distance equals rate times time:


*[tex \LARGE \text{          }\math d = rt]


We can write, for the trip to the retreat:


*[tex \LARGE \text{          }\math d = 50t]


And for the return trip:


*[tex \LARGE \text{          }\math d = 75(10 - t)]


But since the distances are equal, we can write:


*[tex \LARGE \text{          }\math 50t = 75(10 - t)]


Solve this equation for <i>t</i> and then substitute this value in:


*[tex \LARGE \text{          }\math d = 50t]


to get the required distance.


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