Minecraft – Over what distance will one coal power a Minecart with Furnace

One interesting property of the new powered rails are that they act as brakes when no power is applied to them. Because of this, you can make extremely simple stations like this one:

 ▮
▓━─━═━─↔

─ rail       ━ booster rail
▮ button     ═ detector rail
▓ any block

The minecart rests on the slanted powered rail because it the track acts like a brake. When the button is pressed, the track becomes powered and boosts the cart away.

The sequence of detector, powered, detector track isn't a vital part of the station design, but is instead a 2-way booster. When a cart passes over the detector track, the powered rail becomes powered, making a very compact booster. This booster also helps push the cart up the unpowered slanted rail on arrival, resetting it for its next use.

I've been playing around with ways to make a cart magazine that isn't reliant on the cart boosting glitch. However, it's not as simple as constructing something like this...

...as additional minecarts will fall into the bottom one, melding together, instead of stacking.

YouTube user MinecraftAddict developed a hoizontal-cart-magazine-like concept using powered rails like this.

When the redstone is activated, each powered rail will send the cart to the next spot, while the final one will by launched to wherever you hook it up to. However, simply using a button may power the rails for too long and cause some carts to move two spaces, so you may need to use a monostable circuit.

When the button is not pressed, the redstone torch on the side of the button's block keeps the output torch off. When the button is pressed, the first redstone torch turns off, turning the output torch off. At the same time, the repeaters have a redstone signal propagating through them. When the signal finally reaches the output block, the torch turns off again. By adjusting the delay time of the repeaters, you can adjust how long (short) you want the button press to last.

Well, the fastest form of transportation is by minecart, and within The Nether you travel at a 8:1 ratio as in the overworld, so my answer would be traveling via minecart in The Nether.

(Even walking in The Nether is faster than any overworld transportation - minecarts top out at 8m/s, and you certainly walk faster than 1m/s.)