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

Algebra.Com
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(39614)   (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


.
Equation simplifies to




Answer by ikleyn(52756)   (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


 +  = 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.

---------------

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


RELATED QUESTIONS

Solve the problem. A man rode a bicycle for 12 miles and then hiked an additional 8... (answered by checkley77)
a man rode a bicycle for 12 miles and then hiked an additional 8 miles The total time for (answered by josmiceli)
A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time... (answered by ankor@dixie-net.com)
A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time... (answered by josgarithmetic,ikleyn)
Solve the problem. A man rode a bicycle for 12 miles and then hiked an additional 8... (answered by mananth)
A man rode his bicycle for 12 miles and then hiked an additional 8 miles. The total time... (answered by ewatrrr)
A man rode a bicycle for 12 miles and then hiked and additional 8 miles. The total time... (answered by josmiceli)
A man rode a bicycle for 12 miles then hiked an additional 8 miles. The total time for... (answered by josgarithmetic,MathTherapy)
A man rode a bicycle for 12 miles and then hiked on an additional 8 miles. The total... (answered by checkley77)