Proxima Centauri is 4.22 light years. 4.22 light years is about 25 million million miles. At a 1000 miles an hour, that's about 2.85 million years!

Simple 1000 miles an hour is about 447.04 metres per second. The speed of light is 3*10^8 metres per second (300000000). So the speed of light is 671080.89 times larger than the rocket speed you gave. Now Proxima Centauri is generally agreed to be about 4.22 light years away. So if we assume that as soon as you start you instantly hit the speed of light and instantly decelerated at the other end it would take you 4.22 years. Now if we assume you have a rocket that can instantly decelerate/accelerate you then it would take 4.22 * 671080.89 = 2831961.35 years! Or ~2.83 million years! I should point the accuracy I've used here isn't justifiable in such an estimate so that's why I only used two decimal places for my final answer. Sadly it would take much longer than that to get there as you have to first accelerate to your speed of 1000 miles an hour and then decelerate at the other end (or you'll just zip through the proxima centauri system quite fast). This is one of the major headaches with such travel systems as you must first accelerate yourself carrying all the fuel you need to get up to the speed you want and then at the other end slow yourself down. But the longer you take to slow down the longer it takes, and also the faster you go the more energy you need at the other end to stop, which means that you need more fuel which then means your craft is heavier and so you need more fuel at the beginning to get you started. It rapidly becomes quite a headache in such designs. So all in all 2.83 million years is certainly a stretch!

OK, I have changed this answer to reflect the correction that Carnivalius pointed out to me. Assuming an average speed of 1,000 mph and traveling the 4.22 ly to get to Proxima Centauri (not Centaurium): Distance = 4.22ly × 5.879×10^12 mi/ly = 24,809,380,000,000 mi Speed = 1000 mi/h × 24 h/d × 365.24 d/y = 8,765,760.00 mi/yr t = 24,809,380,000,000 mi / 8,765,760.00 mi/yr = 2,830,260 yr I took the numbers for the distances from Wikipedia and used MS Excel to do the math.

I'm lazy - I don't try to work it out myself, I ask Google: 4.5 light years / 1000 mph And I get the answer: 4.5 light years) / (1 000 mph) = 3 017 774.83 years So I reckon Bob B got it rightest.

Did you miss your flight?