SOLUTION: The winner of a 3 mile bicycle race finishes 3 minutes ahead of a teammate and travels on average, 3 miles per hour faster than the teammate. Find the average speed of each racer.

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Question 964974: The winner of a 3 mile bicycle race finishes 3 minutes ahead of a teammate and travels on average, 3 miles per hour faster than the teammate. Find the average speed of each racer.
The faster speed is what?
The slower speed is what?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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S=slower speed; F=faster speed=S+3mph
%283+min%29%281hr%2F60min%29=0.05hr
%283mi%2FS%29-0.05hr=3mi%2FF Substitute for F.
%283mi%2FS%29-0.05hr=3mi%2F%28S%2B3mph%29 Find common denominator for left side.
%283mi%2FS%29-0.05hr%28S%2FS%29=3mi%2F%28S%2B3mph%29
%283mi%2FS%29-%280.05Shr%2FS%29=3mi%2F%28S%2B3mph%29 Combine terms on left.
%283mi-0.05Shr%29%2FS=3mi%2F%28S%2B3mph%29 Cross multiply
%283mi-0.05Shr%29%28S%2B3mph%29=3Smi
3Smi-0.05S%5E2mi%2B9%28mi%29%28mph%29-0.15Smi=3Smi Subtract 3Smi from each side.
-0.05S%5E2-0.15S%2B9=0 Multiply by -20
S%5E2%2B3S-180=0
%28S-12%29%28S%2B15%29=0
S-12=0 or S%2B15=0
S=12 or S=-15
ANSWER 1: The speed of the slower bicycle was 12 mph.
F=S%2B3mph=12mph%2B3mph=15mph ANSWER 2: The speed of the faster bicycle was 15 mph.
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CHECK:
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%283mi%2F12mph%29-0.05hr=3mi%2F15mph
0.250hr-0.05hr=0.20hr
0.20hr=0.20hr