Gears

The front gear on the bike has 32 teeth and the rear, on the wheel, has 12 teeth. How many times does the rear wheel of the bike turns if you turn the right pedal 30 times? What distance will you go if the circumference of the bicycle wheel is 250 cm?

Correct result:

n₂ =  80
s =  200 m

Solution:

$$\begin{gathered} s_1=s_2 \\ {n}_2\cdot 12=32\cdot 30 \\ {n}_2={\displaystyle \frac{32}{12}}\cdot 30=80 \end{gathered}$$

$$\begin{gathered} o=250\text{ cm}\to \text{ m}=250\mathrm{/}100\text{ m}=2.5\text{ m } \\ s=o\cdot n_2=2.5\cdot 80=200\text{ m} \end{gathered}$$

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