Depends on how fast you go
I know that the subject heading of this message seems obtuse, but seriously the distance between North Platte and Grand Junction is about 504 miles. Depending upon the time of day (you hit Denver) and the route you follow thru the mountains, that distance could take as long as 11 hours and as short as 8.
If you follow I-70 (the most direct) and your car can pull the grade at interstate speeds, you can expect to cover this distance in about 8 hours. It is a gorgeous route. Have fun!