That depends on the kayak and the paddler. Short kayaks (under 11 ft.) are not very fast and are typically used for rivers or for short harbor or lake excursions. They are more manoeverable than longer kayaks but not very speedy. Longer boats (say in the range of 16 to 18 feet) are often used for day trips or even touring. They are less manoeverable but faster. The narrower boats are generally faster than wider ones. A typical sustainable pace for a sea kayak in this range is 3 knots for an average paddler in decent shape. You could get one up to perhaps 5 knots on a short sprint. Specialty boats) and surf skis which are usually longer, lighter, and narrower are designed for greater speed but you give up some stability. They require greater skills and balance.
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What is the fastest a kayak or canoe can be paddled?