<PRE><B>Question 772050</B>
The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second. 
Find the speed of the bicycle in feet per second and miles per hour.
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4-inch pedal sprocket rotates at 1 rev/sec
2-inch wheel sprocket rotates at twice the rate of the pedal sprocket=2 rev/sec
14 inch wheel rotates 2/14=1/7 the rate of the wheel sprocket=2/7 rev/sec
..
{{{((2/7) rev/sec)*(2pi(14) inches/rev)*(ft/12 inches)}}}
inches and rev cancel out
(2/7)(28pi)/12=8pi/12=2pi/3=2.09 ft/sec
..
{{{((2pi/3) ft/sec)*(3600 sec/hr)*(mi/5280 ft)}}}
sec and ft cancel out
2pi*3600/3*5280=1.42 mi/hr
..
speed of the bicycle=2.09 ft/sec or 1.42 mi/hr</PRE>