There are actually two times that the car is 60 feet from you. The 1st time (t1) is when it is 60 feet in front of you and the 2nd time (t2) is when it is 60 feet past of you.
Therefore:
60 = 300 – 48 t1
48 t1 = 300 – 60
t1 = 5 seconds
-60 = 300 – 48 t2
48 t2 = 360
t2 = 7.5 seconds
So at 5 seconds and 7.5 seconds