First, we must determine the circumference of the paddle wheel. The formula for the circumference of a circle is: c = 2πr Where r is the radius of the circle. However, we know d = 2r where d is the diameter of the circle. Therefore: c = 2rπ = dπ Substituting 8ft for d gives a circumference of: c = 8πft The time it takes to complete 1 revolution can be found using the formula: t = d/s Where: t is the time it takes: what we are solving for in this problem. d is the distance traveled: we calculated this as 8πft s is the speed traveled: from the problem we know this is 6.7ft/sec Substituting and calculating t gives: t = 8πft / (6.7ft/sec) t = 1.2πsec Two find how long it would take for 100 revolutions we can multiply this time by 100 100 × 1.6πsec ⇒ 122.2πsec If a number is required for the answer we can use 3.14 as an estimate for π giving: 122.2πsec ⇒ 122.2 × 3.14sec ⇒ 383sec
