SOLUTION: a man rode a 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 fast

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Question 147121: a man rode a 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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r%5Bb%5D= rate bicycling in mi/hr
Let r%5Bw%5D= rate walking in mi/hr
It is given that r%5Bb%5D+=+r%5Bw%5D+%2B+10
In words:
Total time for trip = (distance w/bicycle)/(rate on bicycle) +
(distance covered walking)/(rate walking)
5+=+12%2Fr%5Bb%5D+%2B+8%2Fr%5Bw%5D
5+=+12%2F%28r%5Bw%5D+%2B+10%29+%2B+8%2Fr%5Bw%5D
multiply both sides by r%5Bw%5D%2A%28r%5Bw%5D+%2B+10%29
5%2Ar%5Bw%5D%2A%28r%5Bw%5D+%2B+10%29+=+12r%5Bw%5D+%2B+8%2A%28r%5Bw%5D+%2B+10%29
5%2A%28%28r%5Bw%5D%29%5E2+%2B+10r%5Bw%5D%29+=+12r%5Bw%5D+%2B+8r%5Bw%5D+%2B+80
5%2A%28r%5Bw%5D%29%5E2+%2B+50r%5Bw%5D+=+20r%5Bw%5D+%2B+80
5%2A%28r%5Bw%5D%29%5E2+%2B+30r%5Bw%5D+-+80+=+0
divide both sides by 5
r%5Bw%5D%5E2+%2B+6r%5Bw%5D+-+16+=+0
Just by looking at it,
%28r%5Bw%5D+%2B+8%29%28r%5Bw%5D+-+2%29+=+0
r%5Bw%5D+=+-8
r%5Bw%5D+=+2 this is the one that makes sense (it's positive)
r%5Bb%5D+=+r%5Bw%5D+%2B+10
r%5Bb%5D+=+2+%2B+10
r%5Bb%5D+=+12
He hikes 2 mi/hr and bikes 12 mi/hr
check:
5+=+12%2Fr%5Bb%5D+%2B+8%2Fr%5Bw%5D
5+=+12%2F12+%2B+8%2F2
5+=+1+%2B+4
OK