Let's say the distance traveled by car 1 is x miles. Then, the distance traveled by car 2 is (675 - x) miles. We know that distance = rate x time. We are given the rates of car 1 and car 2 as 65 mph and 85 mph, respectively. The time, though unknown, is the same for both cars. We can use the variable t to represent this quantity. We now have the following equations for the two cars:
x = 65t
675 - x = 85t
Let's use the Substitution Method to solve this system of equations. We can substitute the value of 65t for every instance of x in the second equation.
675 - 65t = 85t
675 = 150t
t = 4.5
It will be 4.5 hours before the two cars meet.