Question 282902
Let 

r = rate/speed on the way to the beach
t = time spent traveling to the beach



Since "On the way home, he averaged 10 miles per hour less, and the drive took him one hour longer", this means that his speed back home is {{{r-10}}} mph and the time it took to get back home is {{{t+1}}} hours.



Now using the equation {{{d=rt}}}, we can plug in {{{d=300}}} to get {{{300=rt}}} which is the equation that represents the trip to the beach.



On the way back, the rate is now {{{r-10}}} and the time is now {{{t+1}}} meaning that the next equation is {{{300=(r-10)(t+1)}}}



So you have the correct equations.