SOLUTION: Two cyclists competed in a 5 mile bicycle race. The more experienced cyclist gave the novice cyclist a head start of .6 mile and still won the race by 2 minutes. If the experienced

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Question 729155: Two cyclists competed in a 5 mile bicycle race. The more experienced cyclist gave the novice cyclist a head start of .6 mile and still won the race by 2 minutes. If the experienced cyclist's average speed was 3 mph faster than the novice's average speed, what was the novice's average speed?

Can you please show the work.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Start a stop watch when the experienced cyclist leaves.
Stop it when that cyclist finishes
Let +t+ = experienced cyclist's time to finish
Let +s+ = experienced cyclists average speed
---------------
Novice cyclist's equation:
(1) +5+-+.6+=+%28+s+-+3+%29%2A%28+t+%2B+2%2F60+%29+ ( 2 min is converted to hours )
Experienced cyclist's equation:
(2) +5+=+s%2At+
--------------
(1) +4.4+=+s%2At+-+3t+%2B+%281%2F30%29%2As+-+1%2F10+
and
(2) +s+=+5%2Ft+
(1) +4.4+=+5+-+3t+%2B+1%2F%286t%29+-+1%2F10+
(1) +26.4t+=+30t+-+18t%5E2+%2B+1+-+%283%2F5%29%2At+
(1) +18t%5E2+-+3.6t+%2B+.6t+-+1+=+0+
(1) +18t%5E2+-+3t+-+1+=+0+
use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+18+
+b+=+-3+
+c+=+-1+
+t+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2+-+4%2A18%2A%28-1%29+%29%29%2F%282%2A18%29+
+t+=+%28+3+%2B-+sqrt%28+9+%2B+72+%29%29%2F+36+
+t+=+%28+3+%2B-+sqrt%28+81+%29%29%2F+36+
+t+=+%28+3+%2B+9+%29+%2F+36+
+t+=+12%2F36+
+t+=+1%2F3+
and
(2) +5+=+s%2At+
(2) +s+=+5%2F%281%2F3%29+
(2) +s+=+15+
+s+-+3+=+12+
The novice's speed is 12 mi/hr
check:
(1) +5+-+.6+=+%28+s+-+3+%29%2A%28+t+%2B+2%2F60+%29+
(1) +5+-+.6+=+%28+15+-+3+%29%2A%28+1%2F3+%2B+1%2F30+%29+
(1) +4.4+=+12%2A%28+11%2F30+%29+
(1) +4.4+=+132%2F30+
(1) +132+=+132+
OK