This is more of a fun build. It's not a joke build, but it's more for fun, really. The purpose of building this way is to push out lanes with incredible speed and take out towers in a flash. You can backdoor like nuts with this build, so don't knock it before you try it. Do NOT use this in ranked play. This is best saved for a fun little game on Summoner's Rift or a punishing pushfest in the Proving Grounds. Please enjoy and don't be too offended if this build doesn't seem logical to you. Just try it, tell me what's wrong with it if you feel you must, and chances are I mosty likely already know about said issues.

I'll let you decide which runes to buy since I don't know much about AD runes myself.

I put most of the mastery points in the offensive tree for obvious reasons. I stick the remaining three into reducing the time spent dead, which is always helpful. That is all.

I suggest surge and promote simply to make your turret pushing all the easier. Getting a promoted minion under the turret buys you a lot of time to shoot, while surge increases attack speed and damage to really pack a punch to those turrets or even just to enemies. You can substitute promote for something better like I often do, though, since enemies can take out a promoted minion relatively easily.

Get rocket jump first for escapes. Then max out your explosive shot to help build up farming capability. Max out your ult as soon as possible, of course. Then max rapid fire to boost turret destruction as well as champion damaging. Max rocket jump last as you won't be building AP for it.

Build boots of speed first off for mobility. Then get working on ionic spark. This will give you great attack speed and every four shots you get the burst of lightning that chains up to four targets. This will make farming even faster. Finish berserker's greaves. Move on to tiamat for some AD and sustain but most importantly for its splash damage. This will make every shot do splash damage, plus every fourth shot chains to four targets, plus every minion kill results in an explosion from your explosive shot. Your farm can only get faster from there. Get infinity edge to start dealing tons of damage. With the easy farm, getting enough gold shouldn't be too much of a problem. Then get phantom dancer to up the critical chance which will make infinity edge damage even better, plus the attack speed will help your farming and damage output as well. Round it all off with a bloodthirster to give yourself some sustainability in teamfights and some more damage. Plus, you can get the stacks on it in the blink of an eye.

Here are the pros:
-With all of this combined and used properly, you can push lanes and turrets insanely fast in order to backdoor at the speed of light.
-You will make tons of gold, do lots of scattered damage, and compelte your build very easily.
-Items + rapid fire + surge = dead turret and inhibitor or dead enemies in a teamfight.

Here are the cons:
-Very squishy and easy to focus and kill, shutting down all damage.
-You won't be much of an AD carry until late game since you are designed to push instead. Teamfights are not going to be your strong suit.
-Scattered damage from items make it hard to take out champs one at a time, so plan wisely where you shoot.
-Can easily be stopped by part of enemy team while backdooring if not fast enough or response to you is immediate.