Gears

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

Correct answer:

n₂ =  80
s =  200 m

Step-by-step explanation:

$$\begin{gathered} s_1=s_2 \\ {n}_2\cdot 12=32\cdot 30 \\ {n}_2=\frac{32}{12}\cdot 30=\frac{32\cdot 30}{12}=\frac{960}{12}=80 \end{gathered}$$

$$\begin{gathered} o=250\text{cm}\to \text{m}=250:100\text{m}=2.5\text{m} \\ s=o\cdot n_2=\frac{5}{2}\cdot n_2=2.5\cdot 80=200\text{m} \end{gathered}$$

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