distance between two cities

Question

the distances between cities a and b is 3006 miles less than the distance between c and d if the total mileage is 7824 what is the distance between c and d?

Answer 1

5415.  Let AB represent the distance from A to B and CD represent the distance between C and D.  

 

Then AB + CD = 7824.

 

And CD - AB = 3006.

 

If you add the two equations, AB cancels and you get:

 

2* CD = 10830.

 

Divide both sides by 2 and:

 

CD = 5415