Good morning, Both are correct, but I would say It took me an hour to get to work.

Both are correct

They are both correct, but technically they are slightly different in meaning. It took me an hour to get to work means that that is the length of time you spent traveling. But when you say that you need an hour it refers more to the fact that you are not available for other things, or that the hour is necessary for this. The first statement is more general than the second. For example you can say, "I couldn't offer to drive her to the store because I needed a whole hour to get to work, and giving her a ride would have made me late." Whereas you might say "Wow, today it took me a whole hour to get to work, there was a lot of traffic!" In this sentence you would not use 'I needed' because we are not talking about your needs but about how long it actually took. But most of the time you can use them interchangeably. It is like the difference between "This recipe takes/requires 3 cups of flour" versus "I need 3 cups of flour to make this recipe". You may use them interchangeably, but really the first is just a general statement, whereas the second is applying it to your case. For example, you might think, "I have 5 cups of flour. I need 3 for this recipe... do I have enough also for the other recipe?".