At first at 50 miles/hour he travels 50 miles/hours*3 hours=<<50*3=150>>150 miles.
After that, he speeds up, traveling 80 miles/hours*4 hours= <<80*4=320>>320 miles.
He travels a total of 150 miles+320 miles=<<150+320=470>>470 miles.
He is 600–470=<<600-470=130>>130miles from the hotel.
#### 130