Question

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.

Answer 1

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