Revolutions - wheels

The tractor's rear wheel has a diameter of 1.6 m, and the front wheel is 96 cm. What ratio are the numbers of their revolutions? How many times does the front wheel turn, and how many times does the rear wheel turn on a track 1942 m long?

Final Answer:

r =  5:3
n₂ =  644
n₁ =  386

Step-by-step explanation:

$$\begin{gathered} d_1=1.6\text{m} \\ {d}_2=96\text{cm}\to \text{m}=96:100\text{m}=0.96\text{m} \\ s=1942\text{m} \\ r=d_1/d_2=1.6/0.96\approx 1.6667=5:3 \end{gathered}$$

$$\begin{gathered} o_2=\pi \cdot d_2=3.1416\cdot 0.96\doteq 3.0159\text{m} \\ {n}_2=s/o_2=1942/3.0159=644 \end{gathered}$$

$$\begin{gathered} o_1=\pi \cdot d_1=3.1416\cdot 1.6\doteq 5.0265\text{m} \\ {n}_1=s/o_1=1942/5.0265=386 \end{gathered}$$

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