Using the engines today how long will take humanity to reach earth like planets?
HD 219134b is apparently closest "super earth"; 21 light years away. New Horizons, our speediest yet, is currently running at about 15 km/sec relative to the sun. At 9.46e12 km/lightyear HD 219134b is 2e14 km away At 3.16e7 seconds per year, New Horizons will travel about 4.74e8 km/year. 2e14/4.74e8 = 422000 years.
HD 219134b isn't even a very good earth; gravity is too high.