SOLUTION: A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour fast

                 SPEED           TIME            DIST.
RODE             r+10            12/(r+10)       12
WALK             r               8/r              8
Total                             5

If you read the problem attentively and then think 30 seconds after reading, you may GUESS the solution MENTALLY:


    12 mph cycling and 2 mph hiking.      ANSWER


If you still prefer algebra solution, then write this "time" equation


     +  = 5  hours,


where x is the rate hiking.


To solve this equation, multiply both sides by x*(x+10) and then reduce this equation to the standard quadratic equation form.


Then solve EITHER via quadratic formula OR factoring.


CHECK.   +  = 1 + 4 = 5 hours.