SOLUTION: A man rode a bicycle for 12 miles 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 mph faster than his r
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Question 1010637: A man rode a bicycle for 12 miles 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 mph faster than his rate walking, what was each rate? Found 2 solutions by josgarithmetic, MathTherapy:Answer by josgarithmetic(39614) (Show Source):
The description could be, man rode a bicycle for b miles then hiked an additional h miles.
The total time for the trip was T hours. If his rate when he was riding the bicycle was k mph
faster than his rate walking, what was each rate?
rate time distance
BIKE r+k x b
HIKE r y h
Total T
The given variables are .
The unknown variables are .
Using the basic travel rates rule, x and y can be put into expressions. .
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A man rode a bicycle for 12 miles 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 mph faster than his rate walking, what was each rate?
Let riding speed be S
Then hiking speed = S – 10
Time spent riding:
Time spent hiking:
With total tiem being 5 hours, we get:
12(S – 10) + 8S = 5S(S – 10) ------- Multiplying by LCD, S(S – 10)
(S - 12)(S - 2) = 0
S, or riding speed = mph OR S = 2 (ignore)
Hiking speed: 12 – 10, or mph
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