Question 224089
Time of one car is equal to time of the other car, where time is {{{t=D/r}}}.


Let x = speed of slower car (which travels the shorter distance!)
x+20 = speed of faster car (which travels the longer distance!)


{{{D/r=D/r}}}
{{{240/(x+20)=180/x}}}


Remember that {{{a/b=c/d}}} means {{{ad=bc}}}.


Likewise {{{240/(x+20)=180/x}}} means {{{240x=180(x+20)}}}

{{{240x=180x+3600}}}


Subtract 180x from each side:
{{{60x=3600}}}
{{{x=60}}} mph  speed of slower car
{{{x+20=80}}} mph   speed of faster car


Check:  The faster car travels 240 miles at 80 mph = 3 hours
The slower car travels 180 miles at 60 mph = 3 hours.


R^2


Dr. Robert J. Rapalje