Car tire raduis of 14 in is rotating at 780 revs per min. Find speed of car to nearest mph

Question

A car with a tire of radius 14 inches is rotating at 780 revolutions per minute. Find the speed of the automobile to the nearest mile per hour. 

Answer 1

Every time the car tire turns one revolution, the car moves forward a distance of one tire circumference.

 

The circumference = 2πr = 2π14 = 28π inches.

 

In one minute, 780 revolutions, so the car moves 780 x 28π inches/minute,

 

and in one hour, 60 times that result:

 

60 x 780 x 28π inches/hour

 

Divide that by the number of inches in a mile (1760 yards x 36 inches = the number of inches in a mile) and that should be the speed in miles per hour.