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4 August, 16:17

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.

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Answers (1)
  1. 4 August, 16:27
    0
    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
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