Question 872238
RT=D for rate, time, distance.
Assign some variables, and set a data table.


The description is slightly confusing, but Meri seems to start late.  Fifteen minutes is {{{1/4}}} hour.  Meri seems to run for less time than Cate.  



________________speed_________time__________distance
Cate____________4_____________t+1/4_________4(t+1/4)=d
Meri____________6______________t____________6t=d


d is distance for which Cate and Meri match, or for which Meri catches up with Cate.  t is time in hours that Meri runs when she catches up with Cate.


Both distances are the same.
{{{highlight_green(4(t+1/4)=6t)}}}.


One might assume that you had some mistakes in analyzing the problem and developing a correct equation allowing the solution.  You would solve the shown equation for t.