Mathematics: Two cars leave an intersection at the same time. One drives east while the other travels south at 15 miles per hour faster than the other. After 3 hours, the cars are 225 miles apart. How fast is the southbound car driving?

Two cars leave an intersection at the same time.

villatoroo84502

30.01.2022

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:

$D_E=3E\\D_S=3S=3(E+15)\\D_S=3E+45$

The distance between both cars is given by:

$D^2=D_S^2+D_E^2\\225^2=(3E+45)^2+(3E)^2\\50,625=9E^2+270E+9E^2+2,025\\18E^2+270E-48,600=0\\$

Solving the quadratic equation for the velocity of the eastbound car:

$18E^2+270E-48,600=0\\E^2+15E-2,700\\E=\frac{-15\pm\sqrt{15^2-4*1*(-2,700)}}{2}\\E=45.0\ mph$

The velocity of the southbound car is:

$S=E+15=45+15\\S=60\ mph$

The southbound car is driving at 60 mph.

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