Question 1128942
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<pre>
Let r is the rate biking, in miles per hour.

Then the rate hiking is (r-10) mph.


Your time equation is


{{{12/r}}} + {{{8/(r-10)}}} = 5   hours.       (*)


The answer is obvious and you can get it mentally:  the rate biking is 12 mph; the rate hiking is 2 mph.


If you want to get a formal algebra solution, you can multiply eq(*)  by r*(r-10) (both side) and then solve the obtained quadratic equation.
</pre>

Solved.


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<U>Be aware</U> : the solution by @josgarithmetic is WRONG: his basic equation is written INCORRECTLY.