I felt the same way when I watched episode #6214 of Star Trek the Next Generation. Picard said that the Hera’s last known position was 300 light years away. Geordi said the Hera was in this system 10 days previously. According to the Star Trek Encyclopedia, the time it would take to travel 300 light years at the maximum cruising speed would be approximately 2 months. (if my math is correct). Though they may have either shaken the engines apart to get that far so quickly, or used a wormhole or something.
The catch-all get-out in any flavour of Star Trek is to 'reverse the polarity'...Geordi does it all the time: 'If we reverse the polarity on the short wave tachyon emitter, we can create a gravitational sine wave disruption with the deflector dish which will accelerate the quantum fission ratio of the positronic neutrinos in the hybrid flux drive and interfuse the ambient solar radiation with the exhaust particles from our warp nacelles, creating a space time reverb anomaly...if the nano-molecular stasis pods hold, it could work."
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