I started on my bicycle at 7 am to reach a certain place. After going a certain distance, my bicycle went out of order. Consequently, I rested for 35 minutes and came back to my house walking all the way. I reached my house at 1 pm. If my cycling speed is 10 kmph and my walking speed is 1 kmph, then on my bicycle I covered a distance of :

Time taken :
= 5 hrs 25 min
= $$\frac{65}{12}$$ hrs
Let the required distance be x km
Then,
$$\eqalign{ & \Leftrightarrow \frac{x}{{10}} + \frac{x}{1} = \frac{{65}}{{12}} \cr & \Leftrightarrow 11x = \frac{{650}}{{12}} \cr & \Leftrightarrow x = \frac{{325}}{{66}} \cr & \Leftrightarrow x = 4\frac{{61}}{{66}}{\text{ km}} \cr} $$