Question

Mr. Electron is about to head home after a hard day at work.   His usual route is 10 mm long, but he can also take a short-cut that is only 9.5 mm long.  
(He's an electron!  The distances are short!) 
If he strolls along at his usual 0.725 m/s, why can Mr. Electron never arrive home?    How can he succeed if he is stubbornly fixed on only traveling at 0.725 m/s?  

Answer 1

Mr. Electron can not arrive only in one case if he is on the wrong way. There is nothing to say that he can't arrive at home.

You can see both the routes takes him approximately 3 hrs to reach home.

There is some ambiguity in the question in my opinion.