SOLUTION: A man rode a bike for 12 miles and hiked 8. Total time for the trip was 5 hours. If his rate when he was riding a bike was 10mph faster than his rate walking, whay was each rate?

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Question 32535: A man rode a bike for 12 miles and hiked 8. Total time for the trip was 5 hours. If his rate when he was riding a bike was 10mph faster than his rate walking, whay was each rate?
Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the speed of walking as x mph; speed of biking is then (x+10) mph
Time to hike for 8 miles = 8/x hours
Time to bike for 12 miles = 12/(x+10) hours
Per question, 8/x + 12/(x+10) = 5
=> 8x+80+12x = 5x(x+10)
=> 20x+80 = 5x^2 + 50x
=> 5x^2 + 30x - 80 = 0
=> x^2 + 6x - 16 = 0
=> (x+8)(x-2) = 0
=> x=2 (because speed cannot be -ve)
Answer: Hiking rate was 2 mph and biking rate was 12 mph.