The key here is that the linear velocity of the chain must be the same on both sprockets. 30 rpm = angular velocity of 60pi radians/min; linear velocity = radius* angular velocity = 240pi inches/min.
Working backward on the 2" sprocket, we get an angular velocity of 120pi radians/min which equals 60 rpm.
The bicycle tire is also rotating at 60 rpm which equals 120pi radians per minute which equals a linear velocity of 120pi*13 = 1560pi inches/min. If you want the speed in miles per hour
1560pi inches/min(60min/hour)(1ft/12inches)(1mi… = 4.64 mph.