I saw that Google is putting up $20M dollars as a prize for landing a rover on the moon. (See http://www.googlelunarxprize.org/) I was wondering if that were remotely worth the effort.

You can just hire a company to put a satellite in orbit. The Falcon 9 is supposed to be “the lowest cost per pound to orbit” and it costs $35M to put a small satellite into geosynchronous transfer orbit. Of course the Falcon 9 doesn't actually exist yet, but if it did, you'd only start out $15M in the hole.

Part of the problem of a rocket is that you spend a lot of the energy lifting the fuel and oxygen to the altitude where you plan to use them. I was daydreaming a way to avoid that. If you use a ramjet or scramjet for the lower altitudes, you can use the existing oxygen in the air. This cuts the amount of lifting you have to do by half. Now if you could just figure out a way to get the fuel to where you need it without having to carry it with you.

My initial infeasible idea was to have a long hose.

But then I was thinking that you don't really need a hose to keep the fuel confined. If you squirt a droplet or two of fuel in the path of the oncoming jet, it can be sucked into the intake just like the oxygen. It shouldn't be that hard to time it right. Of course it wouldn't be possible to build a tower tall enough to make this useful, but maybe if you put the tower on the side of a mountain so you can get a few miles of thrust before you have to use the internal fuel supply.