SOLUTION: Ryan travels 10 miles on his bike in the same amount of time that it takes Seth to travel 7.5 miles on his mountain bike. Ryan travels 3 miles per hour faster than Seth. Find eac

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Ryan travels 10 miles on his bike in the same amount of time that it takes Seth to travel 7.5 miles on his mountain bike. Ryan travels 3 miles per hour faster than Seth. Find eac      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 959292: Ryan travels 10 miles on his bike in the same amount of time that it takes Seth to travel 7.5 miles on his mountain bike. Ryan travels 3 miles per hour faster than Seth. Find each speed
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hours for both bikers
Ler +s+ = Seth's speed in mi/hr
Ryan's equation:
(1) +10+=+%28+s%2B3+%29%2At+
Seth's equation:
(2) +7.5+=+s%2At+
-------------------
(2) +t+=+7.5%2Fs+
Substitute (2) into (1)
(1) +10+=+%28+s%2B3+%29%2A%28+7.5%2Fs+%29+
(1) +10+=+7.5+%2B+22.5%2Fs+
(1) +10s+=+7.5s+%2B+22.5+
(1) +2.5s+=+22.5+
(1) +s+=+9+
and
+s+%2B3+=+12+
----------------
Seth's speed is 9 mi/hr
Ryan's speed is 12 mi/hr
-----------------------
check:
(1) +10+=+%28+9%2B3+%29%2At+
(1) +10+=+12t+
(1) +t+=+5%2F6+ hrs
and
(2) +7.5+=+9t+
(2) +t+=+7.5%2F9+
(2) +t+=+5%2F6+
OK