A paddle wheel on a boat is 12 feet in diameter. The fins along the outer edge travel at

a speed of 7.2 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

=

2

π

r

Where

r

is the radius of the circle.

However, we know

d

=

2

r

where

d

is the diameter of the circle.

Therefore:

c

=

2

r

π

=

d

π

Substituting

12

ft

for

d

gives a circumference of:

c

=

12

π

ft

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

12

π

ft

s

is the speed traveled: from the problem we know this is

7.2

ft

sec

Substituting and calculating

t

gives:

t

=

12

π

ft

7.2

ft

sec

t

=

12

π

ft

sec

7.2

ft

t

=

12

π

ft

sec

7.2

ft

t

=

12

π

sec

7.2

t

=

1

.

¯

6

π

sec

Two find how long it would take for 100 revolutions we can multiply this time by

100

100

*

1

.

¯

6

π

sec

⇒

166

.

¯

6

π

sec

If a number is required for the answer we can use 3.14 as an estimate for

π

giving:

166

.

¯

6

π

sec

⇒

166

.

¯

6

*

3.14

sec

⇒

523

sec