SOLUTION: A man rode a bicycle for 12 miles and then hiked and additional 8 miles. The total time for the trip was 5 hours. If his rate when riding a bicycle was 10 miles per hour faster tha

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A man rode a bicycle for 12 miles and then hiked and additional 8 miles. The total time for the trip was 5 hours. If his rate when riding a bicycle was 10 miles per hour faster tha      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 528170: A man rode a bicycle for 12 miles and then hiked and additional 8 miles. The total time for the trip was 5 hours. If his rate when riding a 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 +w+ = rate walking
Let +b+ = rate biking
given:
+b+=+w+%2B+10+ mi/hr
+t%5Bw%5D+%2B+t%5Bb%5D+=5+ hrs
--------------------
biking:
+12+=+%28+w+%2B+10+%29%2At%5Bb%5D+
walking:
+8+=+w%2At%5Bw%5D+
-------------------
By substitution:
+t%5Bb%5D+=+5+-+t%5Bw%5D+
+12+=+%28+w+%2B+10+%29%2A%28+5+-+t%5Bw%5D+%29+
+12+=+5w+%2B+50+-+w%2At%5Bw%5D+-+10t%5Bw%5D+
By substitution again:
+12+=+5w+%2B+50+-+8+-+10t%5Bw%5D+
Substitution again:
+12+=+5w+%2B+50+-+8+-+10%2A%288%2Fw%29+
+80%2Fw+-+5w+=+30+
+80+-+5w%5E2++=+30w+
+w%5E2+%2B+6w+=+16+
Completing the square:
+w%5E2+%2B+6w+%2B+%286%2F2%29%5E2+=+16+%2B+%286%2F2%29%5E2+
+w%5E2+%2B+6w+%2B+9+=+16+%2B+9+
+%28+w+%2B+3+%29%5E2+=+25+
+w+%2B+3+=+5+
+w+=+2+ ( can't use the negative root )
and
+b+=+w+%2B+10+
+b+=+12+
His speed biking was 12 mi/hr
His speed walking was 2 mi/hr