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It depends on how you plan to get there and whether you want to land or just circle and return to earth.
The straight line distance from the earth to the moon is about 250,000 miles but you cannot travel in a straight line because the moon is constantly moving around the earth so you have to aim at a point where the moon will be when your spacecraft also arrives.
Most trips to the moon have involved first orbiting earth, then launching the spacecraft out of earth's gravitational field toward the moon. To escape earth's gravity, you must reach a minimum speed of 25,000 mph. Once you reach that speed you have to decide if you will cut off your engine and continue coasting toward the moon - taking more than 10 days one way - or continue to accelerate to a much higher speed to reach your destination sooner. The Apollo astronauts reached a speed of about 100,000 mph initially and then gradually slowed due to the pull of earth's gravity.
But you cannot go too fast or the moon's gravity will not capture you as you near your target and you will continue off into space forever. That is the process used to get a gravity boost when probes are launched to distant parts of our solar system. So the faster you go at the start of your trip, the more you will have to slow down at the end of the trip so you don't go past your destination.
It all comes down to how much you want to spend speeding up to get there faster vs. going slower but needing more supplies and being exposed to the dangers of space for a longer period of time.
It totally depends on the latest spacecraft technology. Apollo 11 used only 3 days to reach the moon before landing on the moon's surface the next day. With newer and more efficient technology, the journey will also be faster.
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