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.

375 seconds.

Step-by-step explanation:

Step 1

The first step is to find the Circumference of the paddle.

The Circumference of a paddle = Circumference of a circle = 2πr or πD

Where D = Diameter of the circle or Diameter of the paddle

In the question above,

Diameter of a paddle = 8 feet

Circumference of the paddle = πD

= π * 8

= 25.132741229 feet

Step 2

We have to find out first, the time it would take for the paddle to complete one revolution.

This is calculated using the formula:

Time (t) = distance travelled : Speed travelled by the fins along the outer edge of the paddle

In the question,

Speed travelled by the fins along the outer edge of the paddle = 6.7 feet per second

It is important to note that the distance travelled is = Circumference of the paddle = 25.132741229 feet

Time taken to complete one revolution = 25.132741229 feet : 6.7 feet per second

Time taken to complete one revolution. = 3.7511554073 seconds

Approximately = 3.75 seconds.

Step 3

If, 1 full revolution of the paddle takes = 3.75 seconds

100 revolutions =

100 * 3.75 seconds

= 375 seconds.

Therefore, it takes the paddle wheel 375 seconds to complete 100 full revolutions.