Imagine a coordinate plane in your mind.
The origin of this coordinate system is the point (0,0).


The original coordinate of the first car is (0,0).

Its current position at the time moment "t" is  (0,-40t), in kilometers
where t is in hours.



The original coordinate of the second car is (-60,0).

Its current position at the time moment "t" is  (,), in kilometers
where t is in hours.


The difference in x-coordinates is dx = .

The difference in y-coordinates is dy = .


The square of the distance is  

     = (dx)^2 + (dy)^2 =  + 

        = 3600 -  +  + 1600*t^2 -  +  = 

        = 3600 -  +  = 3600 -  + .    (1)


d is minimal where the quadratic form  is minimal.


The quadratic form    is minimal at  t = ,  where b is the coefficient of the form  at t,
while "a" is the coefficient of the form d^2 at t^2.  So,

     =  =  = 1.669 hours (approximately).



To find the value of minimum d,  substitute t = 1.669  hours into the formula (1).  You will get

     =  = 61.0765.



Now the last step to find the value of the minimum distance

      =  =  = 7.815 km.



ANSWER.  The minimum distance between the cars is 7.815 km  (approximately)

         at the time moment t =  hours = 1.669  hours  (approximately).