SOLUTION: A man rode his 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 the bicycle was 10 miles per hour

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Question 1128942: A man rode his 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 the bicycle was 10 miles per hour faster than his rate walking, what was each rate?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
          SPEEDS       TIMES             DISTANCE

BIKE         r +10    12/(r+10)            12

WALK        r            8/r                8

TOTAL                     5

12%2F%28r%2B10%29%2B8%2Fr=5
.
Equation simplifies to r%5E2%2B6r-16=0

%28r%2B8%29%28r-2%29=0

highlight%28r=2%29

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let r is the rate biking, in miles per hour.

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


Your time equation is


12%2Fr + 8%2F%28r-10%29 = 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.

Solved.

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