Cruising along at just Warp 3 would mean we could catch it in just over half an hour.
It is about 12 billion miles out.
Warp 3 is 27 times the speed of light.
You’re using the TOS formula, the TNG formula would put Warp 3 at 38.94 times the speed of light. More bang for the buck with Geordi. Then again, I think Scotty was just underestimating all along!
That’s on the old scale, on the new (TNG) one it’s about 39 times the speed of light.