Please show me the eqution set up for this problem I know it

Please show me the eqution set up for this problem. I know it is d=rt but I don\'t know how to write it out. On one web site I read it said I could not add the rates. Now im really confused been looking for hours for help. Tried to figure it like this
300+150=1000
450x=1000
divide both sides by 450
x=2.22
but when i try to check my problem 450(2.22)=999 not 1000?
Please help!
The problem: Two planes leave the same airport at the same time, flying in opposite directions. The rate of the faster plane is 300 miles per hour. The rate of the slower plane is 150 miles per hour. After how many hours will the planes be 1000 miles apart?

Solution

The exact answer is rational number, 20/9
You used an approximation of this number 2.22
2.222 is more accurate and 2.2222 is mare accurate still, but you never get exactly 1000 when you check the answer unless you use 20/9