Answer
The rear wheel makes $974$ revolutions.
Work Step by Step
We call the distance each wheel makes during the ride $d$. The wheels follow rolling motion, so we have
- Front wheel: $d=s_{front}=r_{front}\theta_{front}$
- Rear wheel: $d=s_{rear}=r_{rear}\theta_{rear}$
Therefore, $$r_{front}\theta_{front}=r_{rear}\theta_{rear}$$ $$\theta_{rear}=\frac{r_{front}\theta_{front}}{r_{rear}}$$
$r_{front}=1.2m$, $r_{rear}=0.34m$ and $\theta_{front}=276rev\times(\frac{2\pi rad}{1rev})=1734.16rad$
Therefore, $$\theta_{rear}=6102.56rad\times\Big(\frac{1rev}{2\pi rad}\Big)=974\text{ revolutions}$$
