How to solve the 2 cars math problem

If two cars were faced away from each other back to back, both cars travelled 8 miles forward then made a 90 degree left turn and traveled another 6 miles, how far apart would they be?

Possible answers (as given on question):

� Right next to each other.

� 48km

� 32km

� I'm not sure / Hey, there's no SKIP button

First we must find how far each car went. If the beginning point is (0,0) on a coordinate plane, the the car on the right went to point (8,6) and the car on the left went to point (-8,-6). They for a diagonal line on opposite sides of the plane so option A (Right next to each other is wrong). We want to find the length of the diagonal so we do the following.

a^2 + b^2= c^2 (the Pythagorean theorem)

a= to the distance on the x axis (or 8) and b= to the distance on the y axis (or 6). Remember, you cannot have negative distance, so even though on of the cars is in the negative portion of the plane, it still went positive distance. C= the unknown diagonal length.

a^2 + b^2= c^2

8^2 + 6^2= c^2

64 + 36 = c^2

100 = c^2

sqrt(100)= sqrt(c^2)

10 = c

c= 10

They are 20 miles away from each other. However, the answers are in km so we convert from mi to km.

1 mile is, approximately, 1.6 km so we do the following:

1 mi/1.6 km = 20 mi/ X km, cross multiply

X= 32

So the distance between the two cars is approximately 32 km, or answer C.