Question 63310
We'll let x=amount of time that will pass before the second cyclist catches up with the first from the time the second cyclist started biking 

Now we know that when the 2nd cyclist starts biking, the first cyclist has already traveled (6)(3) or 18 miles and we also know that when the 2nd cyclist catches up, the first cyclist will have traveled 18+6x miles and the 2nd cyclist will have traveled 10x miles. Obviously, when these two distances are equal, the two cyclists are at the same place on the trail and that's what we are looking for.  So, the equation to solve is:
18+6x=10x or 
18=4x
x=4.5 hours

Hope this helps and have a happy holiday season---ptaylor