A paddle wheel on a boat is 8 feet in diameter. The fins along the outer edge travel at a speed of 6.7 feet per second. How long does it take the paddle wheel to complete 100 full revolutions? Round to the nearest second.

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