SOLUTION: 2 CYCLIST START BIKING FROM A TRAIL START 3 HOURS APART. THE 2ND TRAVELS AT 10 MILES PER HOUR AND STARTS 3 HOURS AFTER THE 1ST WHO IS TRAVELING AT 6 MILES PER HOUR, HOW MUCH TIME

Question 273582: 2 CYCLIST START BIKING FROM A TRAIL START 3 HOURS APART. THE 2ND TRAVELS AT 10 MILES PER HOUR AND STARTS 3 HOURS AFTER THE 1ST WHO IS TRAVELING AT 6 MILES PER HOUR, HOW MUCH TIME WILL PASS BEFORE SECOND CATCHEDS FIRST
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Each cyclist must have their own equation
1st cyclist:

2nd cyclist:

given:
The 1st cyclist has a head start which is
mi/hr x hrs = mi
mi/hr
mi/hr
-----------------------
Assume I have a stopwatch and I start it when
the 2nd cyclist leaves. When I stop the watch
so I'll call them both
The 2nd cyclist has to make up the head start, so
mi
------------------------

(1)
and

(2)
I'll substitute (1) into (2)

hrs
This is the elapsed time after the 1st cyclist got
a hr head start, so
the 2nd cyclist catches the 1st cyclist hrs
after the 1st cyclist left
check answer:

mi
and

and, since

then,

mi
OK