Question 1204447
This part is interesting:  "One cyclist is traveling at 2/3 the rate of the other cyclist."


If one cyclist is going at speed 2Q and the other cyclist goes at speed 3Q, then description allows this:


For the 2 hour to close their distances,  {{{(2Q+3Q)*2=25}}}.

{{{5Q*2=25}}}
{{{2Q=5}}}
{{{Q=2&1/2}}}


The speeds of the cyclists are  5 mph and 7.5 mph.