Question 220538
Assume I have a stopwatch. I will start the stopwatch 
when the sheriff leaves. At that time, Rick has travelled
{{{d[r] = 64*(3/4)}}} (45 min is 3/4 of an hour)
{{{d[r] = 48}}} mi
So, Rick has a 48 mi headstart
From this headstart to where the sheriff catches him,
call {{{d}}} in miles
For the sheriff:
{{{d + 48 = 80*t}}}
For Rick:
{{{d = 64*t}}}
By substitution:
{{{64t + 48 = 80t}}}
{{{16t = 48}}}
{{{t = 3}}}hrs
The sheriff catches him 3 hrs after the sheriff leaves town
check answer:
{{{d = 64t}}} (for Rick)
{{{d = 64*3}}}
{{{d = 192}}} mi
So, Rick went a total of {{{48 + 192 = 240}}} mi at {{{64}}} mi/hr
The sheriff went {{{240}}} mi also at {{{80}}} mi/hr
For Rick:
{{{240 = 64*t[r]}}}
{{{t[r] = 3.75}}} hrs for the whole trip for Rick
For Sheriff:
{{{240 = 80*t[s]}}}
{{{t[s] = 3}}} hrs for the whole trip for Sheriff
Note that {{{3.75 - 3 = .75}}}, which is
the 45 min headstart that Rick had