Question 16 <> 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 185 rpm. Round answers to 2 decimal places as needed. The linear speed of the bicycle in inches per minute in/min The speed of the bike in miles per hour mph %3D

19.28 mph

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

i can try and you the very best that i can.