-- Last Updated: Mar-27-13 9:50 PM EST --
First, the math because that's the easy part. Ignoring the fact that waterline length will be slightly less than boat length, hull speed of a 14-foot boat is 5.76 mile/hour, and that of a 16-foot boat is 6.16 mile/hour (note that it's actually pretty silly to report these speeds to the nearest 0.01 mile/hour, but this is just a math exercise anyway).
When paddled at hull speed the whole time:
The time for the 14-foot boat to finish the race =
13 miles x 1 hour/5.76 miles = 2.26 hours, or about 2 hours and 15 minutes.
the time for the 16-foot boat to finish the race =
13 miles x 1 hour/6.16 miles = 2.11 hours, or about 2 hours and 6 minutes.
Based on that alone, the 16-footer should give you a better time. However, it will take more effort to keep the longer boat at top speed, and no two boats are identical in all respects other than length so any comparison like this is affected by more than what's in this over-simplified way of looking at things. It's also unlikely you'll be strong enough to push either boat at its top speed for the full duration of the race. Still, if both boats were paddled at the identical speed (at least for "fast" speeds), the shorter boat would be closer to its maximum and that would almost certainly require more effort, so a strong paddler should be able to finish the race in substantially less time with the longer boat (on the other hand, the shorter boat will be a bit easier to paddle at slow or moderate speeds, all else being equal). The difference in time between the two boats cannot be predicted with anything close to the degree of accuracy that seems to be implied by the math. Throw in various other factors and it's even possible you'd be faster in the shorter boat, especially if it's a substantially better design than the longer boat, but on average I'd bet on the longer one giving you a quicker time.
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