Question 964974
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S=slower speed; F=faster speed=S+3mph
{{{(3 min)(1hr/60min)=0.05hr}}}
{{{(3mi/S)-0.05hr=3mi/F}}} Substitute for F.
{{{(3mi/S)-0.05hr=3mi/(S+3mph)}}} Find common denominator for left side.
{{{(3mi/S)-0.05hr(S/S)=3mi/(S+3mph)}}} 
{{{(3mi/S)-(0.05Shr/S)=3mi/(S+3mph)}}} Combine terms on left.
{{{(3mi-0.05Shr)/S=3mi/(S+3mph)}}} Cross multiply
{{{(3mi-0.05Shr)(S+3mph)=3Smi}}}
{{{3Smi-0.05S^2mi+9(mi)(mph)-0.15Smi=3Smi}}} Subtract 3Smi from each side.
{{{-0.05S^2-0.15S+9=0}}} Multiply by -20
{{{S^2+3S-180=0}}}
{{{(S-12)(S+15)=0}}}
{{{S-12=0}}} {{{or}}} {{{S+15=0}}}
{{{S=12}}} {{{or}}} {{{S=-15}}}
ANSWER 1: The speed of the slower bicycle was 12 mph.
{{{F=S+3mph}}}={{{12mph+3mph=15mph}}} ANSWER 2: The speed of the faster bicycle was 15 mph.
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CHECK:
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{{{(3mi/12mph)-0.05hr=3mi/15mph}}}
{{{0.250hr-0.05hr=0.20hr}}}
{{{0.20hr=0.20hr}}}