Wikipedia shows the relationship between the orbits of Earth and the asteroid.
https://upload.wikimedia.org/wikipedia/commons/9/96/.Animation_of_Hayabusa2_orbit.gif
The earth’s orbit is about 93 million miles in radius, so when the asteroid is on the opposite side of the sun then it is indeed about 180 million miles away. But the gif shows that the earth keeps “catching up” to the asteroid making that distance considerably less.
As for how long it takes to travel 180 million miles, you do it every four months or so, just by riding the earth along its orbit. Being launched into space doesn’t change that…you still carry the momentum of the earth with you.
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