A bicycle with 18-in.-diameter wheels has its gears set so that the chain has a 6-in. radius on the front sprocket and 3-in. radius on the rear sprocket. The cyclist pedals at 180 rpm.

Step-by-step explanation:

"The question is not complete, here is the complete question

A bicycle with 18-in.-diameter wheels has its gears set so that the chain has a 6-in. radius on the front sprocket and 3-in. radius on the rear sprocket. The cyclist pedals at 180 rpm.

Find the linear speed of the bicycle in in/min (correct to at least two decimal places)  

How fast is the bike moving in mph (to two decimal places)?"

Step one:

given data

the diameter of wheels= 18 inches

radius of front sprocket=6 inches

radius of rear sprocket= 3 inches

The cyclist pedals at 180 rpm

The chains move at the same speed, hence

the rear sprocket must make 6/3 revolutions for every one revolution made by the front sprocket

when the rider moves the front sprocket through 180 revs/min

the rear sprocket moves through 180 (6/3)  = 360 revs/min

the linear speed of the bicycle in inches per minute  =

 2π * 9 * 360   = about 20360.16  in/min

The speed in mph

=2π * 9 * 360 * 60 minutes in 1 hr /63360 in/ mile  

=19.28 mph

answer: the answer is 40.82

step-by-step explanation: 3.14 x 13(or half of 26) to the power of 2