At what rate is the distance between the cars increasing two hours later?

Question

Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing two hours later?

 mi/h

Answer 1

After a time t

the first car will be at the point 48t South of the starting point,

the other car will be at the point 20t West of the starting point.

Since their directions are perpendicular, their distance after time t is

√((48t)² + (20t)²) =

√(2304t² + 400t²) =

52t

Therefore their distance always increases at the constant rate of 52 mi/h.