Question

Luis can drive 3 times as fast as Carlos can ride his bicycle. If it takes Carlos 3 hours longer than Luis to travel 63 miles , how fast can Carlos ride his bicycle?

Answer 1

Let v_C be Carlos' speed and v_L Luis' speed. We're told Luis drives three times as fast as Carlos rides; that is,\[v_{L}=3v_{C}\]Let t be the time, in hours, taken by Luis to travel 63 miles. Then\[v_{L}=\frac{63}{t}miles/hour\]and\[v_{C}=\frac{63}{t+3}miles/hour\]since it takes Carlos 3 hours longer than Luis. Hence, linking the last two equations via the first, we have,\[\frac{63}{t}=3 \times \frac{63}{t+3} {\rightarrow}t=\frac{3}{2}hours\]Substituting this into the second equation, the speed for Carlos' bike, yields what we need,\[v_{C}=\frac{63}{\frac{3}{2}+3}miles/hour=14miles/hour\]