Two cars leave a city, one traveling east and the other west. The car going east is traveling at 64 mph and the car going west is traveling at 60 mph. How long before they are 434 miles apart?

Answer: t = 108.5 hours

Explanation:

We can represent the velocity of the cars as vectors.

Velocity of first car = 64 mph due east

Velocity of second car = 60 mph due west.

Since both vectors are in opposite direction, the magnitude resultant vector is the difference between the 2 vectors in the direction of the larger vector.

Hence, resultant speed = 64 - 60 = 4mph

Direction of resultant speed = east.

They are 434 miles apart, that's the total distance traveled.

But speed = distance / time.

4 = 434/t

t = 434/4 = 108.5 hours

t = 108.5 hours