SOLUTION: marcus and beth leave college traveling in opposite directions on a straight road beth drives 13 mi/h faster the marcus after 4 hours they are 452 miles apart find their rates

Let r be the Markus rate;  then the Beth rate is (r+13) mph.


The total separating distance is  4r + 4*(r+13) miles,

and it is equal to 452 miles.  So your base equation is

    4r + 4*(r+13) = 452  miles.


Simplify and find r

    4r + 4r + 52 = 6730

    8r           = 452 - 52 = 400

     r                      = 400/8 = 50 miles per hour.


ANSWER.  The Markus rate is  50 mph.

         The Beth rate is  50 + 13 = 63 mph.


CHECK.  4*50 + 4*63 = 452 miles separating distance in 4 hours.   ! Correct !