Question 153445
Remember:
{{{speed=x(mi/hr)}}} of the bicyclist and hiker:
{{{hiker=h=x(mi/hr)}}}
{{{biker=b=3x(mi/hr)}}}, 3 times faster
Equating the 2 speeds and adding the speed (separation) of 24 miles in 3 hours to the hiker since the bicyclist is faster than the hiker:
{{{hiker=biker}}}
{{{(x(mi/hr)) +(24mi/3hr)=3x(mi/hr)}}}
{{{(cross(24)8mi/cross(3)hr)=3x(mi/hr)-x(mi/hr)}}}
{{{8(mi/hr)=2x(mi/hr)}}} ----> {{{cross(8)4(mi/hr)=cross(2)x(mi/hr)}}}
{{{x=4(mi/hr)}}} ---------------------> speed of the hiker
For bicyclist:
{{{3*4=12(mi/hr)}}} ------------------> speed of the bicyclist
to check, lets calculate the distance in 3 hours:
hiker: {{{4(mi/cross(hour))(3cross(hours))=12miles}}}
biker: {{{12(mi/cross(hour))(3cross(hours))=36miles}}}
IT'S TRUE THAT AFTER 3 HOURS, THE DISTANCE SEPARATING THEM IS  {{{36-12=24miles}}}
</pre><font size=4><b>Thank you,
Jojo</pre>