SOLUTION: The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 11 miles per hour, how fast would

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Question 1128969: The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 11 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft. Round your answer to the nearest tenth.)

= rpm
Answer by greenestamps(13211) About Me  (Show Source):
You can put this solution on YOUR website!


The diameter is 14 feet; the circumference is 14pi feet.
An hour is 60 minutes.
A mile is 5280 feet.

Use unit conversions to convert rpm to miles per hour; the cable moves at the speed of a point on the circumference of the pulley.
      rev     14pi ft      1 mi      60 min       mi
   x ----- * -------- * --------- * ------- = 11 ----
      min      1 rev     5280 ft      1 hr        hr


x%2A%2814pi%29%2A%281%2F5280%29%2A%2860%29+=+11

x+=+11%2F%28%2814pi%29%2A%281%2F5280%29%2A%2860%29%29 = 22.009

To the nearest tenth, the rate of rotation of the pulley to get a speed of 11 mph is 22.0 rpm.