Answer:
60 mph
Step-by-step explanation:
Let 'S' be the velocity of the southbound car and 'E' be the velocity of the eastbound car. The distances traveled by each car are:
[tex]D_E=3E\\D_S=3S=3(E+15)\\D_S=3E+45[/tex]
The distance between both cars is given by:
[tex]D^2=D_S^2+D_E^2\\225^2=(3E+45)^2+(3E)^2\\50,625=9E^2+270E+9E^2+2,025\\18E^2+270E-48,600=0\\[/tex]
Solving the quadratic equation for the velocity of the eastbound car:
[tex]18E^2+270E-48,600=0\\E^2+15E-2,700\\E=\frac{-15\pm\sqrt{15^2-4*1*(-2,700)}}{2}\\E=45.0\ mph[/tex]
The velocity of the southbound car is:
[tex]S=E+15=45+15\\S=60\ mph[/tex]
The southbound car is driving at 60 mph.
