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

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(39615) (Show Source): You can put this solution on YOUR website!
The same question happens as different examples. This table shows this as a generalization.

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.
.

The given total time T fits with an equation,

Solve the red-outlined equation for r.

Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!

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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