Answer
$146\ in$
Work Step by Step
1. Assume the smaller gear will rotate an angle $\theta^\circ$, we have $1.38\times\theta^\circ\times\frac{\pi}{180^\circ}=4.72\times180^\circ\times\frac{\pi}{180^\circ}$, thus $\theta\approx615.7^\circ$
2. The bicycle will travel a distance of $L=13.6\times615.7^\circ\times\frac{\pi}{180^\circ}\approx146\ in$
