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 $97968$ inches in $15$ minutes. How far (in inches) does a point on the outer edge of the fan travel in $30$ minutes?
We can think of concentric circles, here....if R is the radius from the middle of the fan to the halway point, then 2R is the distance from the center to the edge....thus....in one revolution the center point travels 2piR inches
and the outside point travels 2pi * 2R = 4piR inches = twice as far
In 30 minutes....the center point travels twice as far as it does in 15 minutes = 97968 * 2 = 195,936 inches
And the outside edge will travel twice as far as this = 391,872 inches