Question 818575
The times are known but Ken's rate is unknown.  You know their distances will be equal.


Think in HOURS or fractions of an hour, not in minutes.
Joe goes for h+1/6 hours;
Ken goes for h hours.


R*T=D for Rate, Time, Distance.


{{{6(h+1/6)=r(h)}}}  and {{{h+1/6=(1/2)}}}.
Find the value of h from the second equation and use it in the first equation.  This gives you one equation using only the variable, r.  


{{{h=1/2-1/6}}} but you can see from time on a number line that h is {{{1/3}}} hour.
{{{6(1/2)=r(1/3)}}}
{{{r=6(1/2)(3/1)=highlight(r=9)}}}