A passenger train left the station and traveled west at an average speed of 20 km/h. Sometime later a freight train left traveling in the opposite direction with an average speed of 55 km/h. After the passenger train had traveled for 13 hours the trains were 975 km apart. How long did the freight train travel?

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.