I agree with Garrett.  :)

In addition, please note that in the US, we rarely use the word "speedily" (probably because it just sounds awkward and doesn't flow well?)  This is true in both spoken and written English.

We use "fast" a LOT!!  We also use "quick", but not near as much as "fast".  In my opinion, in the US, we tend to WRITE "quick" more than we speak it.  Our usual spoken word concerning speed is "fast".  

Spoken phrases I may use and hear a lot:

Fast

Lightning fast!

Super fast!

Amazingly fast!

Did you see how fast he was driving?  He just zipped by me like I was going backwards!

Hurry up Suzy and put your shoes away.  You aren't moving  fast enough.

Fast and quick are adjectives.

Speedily is an adverb. Quickly can also be an adverb, but fast cannot become an adverb.
(Speedy is the adjective form of speedily. Fastly is not a word.)

So, naturally, the way you use adverbs and adjectives will be different.  

He quickly finished his homework and then went outside to play. 
He was driving really fast, so he wouldn't be late to work. 

She got dressed speedily and rushed out the door. 

In my opinion, I think adverbs can be used to describe that the process was finished in a short amount of time. 
But the adjectives "fast/quick/speedy" seem to focus on the fact that the person was operating at a high speed, but not necessarily finishing in a short amount of time, even though the meaning was implied. 

For example, you can drive fast. 
You can get home quickly. 

You can flip the two and it still makes sense and people say it in that way, but, to me, it sounds better to distinguish like that.

Basically, they have almost the same meaning, just know when to use an adverb and when to use an adjective and you will be ok :)

Sorry if that was confusing.