They will lose contract after ___ hrs

Question

A truck and car leave a service station at the same time and is traveling also in the same direction. The truck travels at 60 mph and the car at 54 mph. They can maintain radio contact within a range of 12 miles. When will they lose contact?

 

 They will lose contract after ___ hrs

(Type an integer or a decimal.)

Answer 1

In T hours the truck will travel 60*T miles and the car will travel 54*T miles  

The distance between them will be 60*T - 54*T = 6*T

This distance will equal 12 miles when 6*T = 12  ==>  T = 2 hours  

 

You can also solve this problem using the principles of relativity (that's right, relativity - it's not just for Einsteins anymore).  If you look at the way things are changing relative to the car (this is called the car's frame of reference) then the car is not moving relative to the car (obviously) and the truck is moving away from the car at a relative speed of 60 - 54 = 6 mph.  So in the car's reference frame it will take the truck (12 miles / 6 mph) = 2 hours to move 12 miles away from the car and lose radio contact.