Question

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.

How many minutes and seconds?Ex: 3 minutes and 23 seconds

Answer 1

See a solution process below:

Explanation:

First, we must determine the circumference of the paddle wheel.

The formula for the circumference of a circle is:

`c = 2pir` Where `r` is the radius of the circle.

However, we know `d = 2r` where `d` is the diameter of the circle.

Therefore:

`c = 2rpi = dpi`

Substituting `12"ft"` for `d` gives a circumference of:

`c = 12pi"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 `12pi"ft"`

`s` is the speed traveled: from the problem we know this is `(7.2"ft")/"sec"`

Substituting and calculating `t` gives:

`t = (12pi"ft")/((7.2"ft")/"sec")`

`t = (12pi"ft"" sec")/(7.2"ft")`

`t = (12picolor(red)(cancel(color(black)("ft")))" sec")/(7.2color(red)(cancel(color(black)("ft"))))`

`t = (12pi"sec")/7.2`

`t = 1.bar6pi"sec"`

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

`100 xx 1.bar6pi"sec" => 166.bar6pi"sec"`

If a number is required for the answer we can use 3.14 as an estimate for `pi` giving:

`166.bar6pi"sec" => 166.bar6 xx 3.14"sec" => 523"sec"`