First you have to make the assumption that these are the only two outcomes. There is also the possibility of hitting the ball and getting out.
However, if we assume that these are the only two cases, we know that the probability is 58.3%. This is because it has been on base 7 times out of 12.
If the average rates were 20 and 25 miles per hour, then together they cover 45 miles of the distance they are separated by per hour. The ships will be 30 miles apart when 270 miles have been covered, so it takes 270/45=6 hours to cover the distance. 6 hours after 5 PM is 11:00 PM.
THIS IS THE CORRECT ANSWER I GOT WHEN SOLVING ON MY IPHONE