An express train and a local train both leave Lake City at 12:00 noon and head for Chicago 60 miles away. The express train travel twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train.

MY SET UP:

Express Train:

rate = 2x + 2

distance = 60 miles

time = 12

Local Train:

rate = x

distance = 60 miles

time = 12

My equation:

12(2x + 2) + 12x = 60

Is this the right equation? If not, what did I do wrong?