I want to turn my bike into an electric bike.

1 - Usual solution: I've been researching and a 500W / 24V engine of 250 rpm and torque of 19Nm, suitable for electric bicycles, costs from R $ 400,00 here in Brazil. It would have to be connected in two 12V batteries in series (which cost at least R $ 70.00 each).


2 - My idea: To use a 500W / 127V 900 rpm lawn mower motor (which costs R $ 100.00) in a 12-tooth pinion, with a chain going from the pinion of the motor to the pinion, where the pedals , of the bicycle with about 50 teeth. This, according to the physics, would lead to a reduction of speed in 4 times and increase of the motor torque in 4 times. The motor power would be made by two 12V parallel batteries connected in a 12V to 127V inverter that supports 500W and costs R $ 70.00

3 - My calculations:
Power (W) = Torque (Nm) * Angular velocity (rad / s)
Knowing that 1rpm = 0.105 rad / s

500W / 12V motor that costs R $ 400,00:
500 = 19x250x0.105
Soon:
500 = 498.75 Ok

Lawn Mower Engine That R $ 100.00
500 = Tx900x0.105
Soon:
T = 5 Nm

However, with the ratio of the pinions: T = 5x4 = 20 Nm and speed = 900/4 = 225 rpm
What would be very similar to the 24V motor

4 - My Conclusion: I believe that with 20Nm it is possible to carry 120kg (50kg of the bike + 70kg of a person). And with 225rpm it is possible to reach 25km / h. What do you think?