A circular ceiling fan rotates at a constant speed of 80 revolutions per minute. A point halfway between the center of the fan and the outer edge of the fan travels 90 inches in 2 minutes. How far (in inches) does a point on the outer edge of the fan travel in 30 minutes?
+128473 If the halfway point fan travels 90 in in 2 min.....then it must travel 45 in in one minute
So we can find the radius of this "smaller " circle that the halfway point travels through as
45 = 80 * 2pi * r
45 = 160 pi * r
45 / ( 160 pi) = r = 9/ (32 pi) in
And a point at the outer edge must travel on a circle with a radius of twice as much = 9 / ( 16 pi) in
So.....the total distqance that this point travels in 30 min =
(No. of revs in 30 min) * ( 2 pi ) * (r) =
30 ( 80) ( 2pi) ( 9 / (16 pi) ) = 2400 * 18 * (9/16) = 2700 in
