Answer:
13 m
Step-by-step explanation:
You want to know the distance traveled using a 52-tooth chainring and 12-tooth sprocket if a 42-tooth chainring together with an 18-tooth sprocket lets you travel 7 meters per pedal revolution.
The number of revolutions the wheel makes is the number of pedal revolutions multiplied by the ratio of teeth in the chainring to teeth in the sprocket.
The 42-tooth chainring and 18-tooth sprocket multiplies the pedal revolutions by 42/18 = 7/3.
The 52-tooth chainring and 12-tooth sprocket multiplies the pedal revolutions by 52/12 = 13/3.
Assuming no change to wheel diameter, the distance traveled is proportional to the pedal multiplier, so we have
x/(7 m) = (13/3)/(7/3) = 13/7
x = 13 . . . . . . . . . . . . . . . . . . . . multiply by 7
The travel with the 52-tooth chainring will be 13 meters per pedal revolution.
