SOLUTION: Car A takes 15 seconds to go once around a circular racetrack, and car B takes 25 seconds to go once around the same track. If the two cars begin racing from the same position at t

Let D be the length of the track.

    (As you will see from the solution, the value of D does not participate in the solution; 
     so it does not matter even in which linear units we measure D).


Then  the speed of the faster track is  linear units per second,
while the speed of the slower track is  linear units per second.


The condition that the faster car will pass/overtake the slower is that the faster car will travel the distance 
    exactly D units longer than the slower track, or

 -  = D.


After canceling the factor D in both sides this equation takes the form

 -  = 1.


Simplify and solve for "t".  First step is to multiply both sides by 75:

5t - 3t = 75 ====>  2t  = 75  ====>  t =  = 37.5 seconds.


Answer.  The faster car will pass/overtake the smaller car in 37.5 seconds.