let

x = the distance from A to B

y = the distance from C to D

the distance from city A to city B is 3006 miles less than the distance from City C to City D:

x = y - 3006

the total of these two distances is 7834 miles:

x + y = 7834

by solving the system of equations:

x = y - 3006

x + y = 7834

we find:

x = 2,414 mi

y = 5,420 mi

click here to see the step by step solution of the system of equations:

the distance from City C to City D is 5,420 miles.