Name: Tom Who is asking: Other Level: All Question: A ship goes in one direction, west to Hawaii, at 20 nautical miles per hour and, because of the wind, makes the return trip at 30 nautical miles per hour. What is the average speed? Thanks in advance, Tom Hi Tom, The naive answer is just the average of the speeds: (20 + 30)/2 = 25 nautical miles per hour. Perhaps surprisingly, this turns out to be the wrong answer: The ship will travel a longer time at 20 nautical miles per hour on the way to Hawaii than at 30 nautical miles per hour on the way back (because it is then going faster); therefore the average speed should be closer to the slower speed than to the faster speed: less than 25 nautical miles per hour. The right way to look at the problem is to consider a stretch of 60 nautical miles: it took 3 hours to cross it from east to west at 20 nautical miles per hour, and then on the way back it took 2 more hours to cross it from west to east at 30 nautical miles per hour. This gives us a total of 120 nautical miles covered in 5 hours. What was the average speed? Would you get a different answer if the distance were something other than 60 nautical miles? Cheers, Claude Go to Math Central