Acar leaves a town traveling at 60 miles per hour. two hours later, a second car leaves the town traveling the same route and overtakes the first car in 6 hours and 40 minutes. how fast was the second car traveling?

After two hours, the first car has traveled (2 x 60) = 120 miles.
That's the gap that the second car has to close.

The second car closes the gap of 120 miles in 6-2/3 hours.
He must have exceeded the first car's speed by (120/6-2/3) mph.

6-2/3 = 20/3

120 divided by 20/3  =  120 x 3/20 = 360/20  =  18 mph

The second car exceeded the first car's speed by 18 mph,
so he had to be traveling (60 + 18) = 78 mph to catch up.

Check:

In 6-2/3 hours . . .

The first car covers  (60 x 20/3) = 400 miles.

The second car covers  (78 x 20/3) = 520 miles.
This is the same distance as the first car PLUS the 120
that he was behind when he started out.
                                                                     yay !