At 800 am the smiths left a campground driving at 48 mihour

At 8:00 am the smiths left a campground driving at 48 mi/hour. At 8:20 the Garcias left the same campground and followed the same route driving at 60 mi/hour. At what time did they overtake the Smiths?
I thought that I had to take 20/60 to get 1/3, to make minutes into hours, and add it to 60t. Then have 48t equal that. (Shown Below)
48t = 60(t+1/3)
Then, I distributed, and got:
48t = 60t + 20
I subtracted 60t from 48t, and got this:
-28t = 20

Solution

they overtake when they have travelled the same DISTANCE (rate x time)

the shorter time goes with the faster speed

60 t = 48 (t + 1/3) ___ the Smiths had a 20 min head start

12 t = 16 ___ t = 4/3 or 1:20

8:20 + 1:20 = 9:40