Distance/Rate/Time equation

Last question of the day, I promise! lol...

I am having a real hard time translating word problems having to do with distance and time. I dont understand the concept of it for some reason.. The problem I am trying to solve is this:

"On a 300 mile trip to Chicago, Josh drove part of the time at 60 mph and the remainder of the trip at 70 mph. If the total trip took 4.5 hours, for how many miles did Josh drive at a rate of 60 mph?"

Can someone teach me how you are supposed to set these problems up? My teacher gave us the equation 60x + 70(4.5 - x) = 300, but I dont understand how we get there.

why are we subtracting 4.5 (time) from the miles driven (x)? I dont get it...