Question 1087708
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<U>Answer</U>.  The speed of the bicyclist going uphill is 12 mph.


<U>Solution</U>


<pre>
Let u be the speed of the bicyclist going uphill, in mph.


Then  the speed of the bicyclist going downhill is (u+12) mph.


Your "time equation" for the round trip is

{{{12/(u+12) + 12/u}}} = {{{3/2}}}  hours.


Solve for u and get the answer.
</pre>