I will say that your translation "To where are you running?" is far less common in everyday English, to the point that a person might look at you funny if you asked it conversationally. (Also, the proscription against ending an English sentence with a preposition is not followed by various major publishing houses.)
This app accepts more than one answer if the answers are both acceptable. To where are you running may not be usual but nevertheless it is correct and should be accepted. We cannot possibly know whether they are looking for the normal usage or the correct grammar before we answer so it is only reasonable to accept both. That way we can all be happy!
Totally agree that both should be accepted. I'm a little sad that, having had my natural (British) English way of translating phrases rejected by Duolingo several times now, I was trying so hard to use 'proper grammar' and avoid that hanging preposition but it totally backfired...
Interesting information, DottyEyes. I wasn't previously aware of the publishing house stance on this, but I have been taught the rule about not ending a sentence with a preposition. Though I generally try to avoid it, at times it just sounds so ridiculous and pompous to try to do so. Whenever I buck the rule, however, I always wonder if some asinine "grammar Nazi" with just a little bit of knowledge and little common sense when it comes to the affects of the written word is going to judge my writing poorly for it.
Actually, a quick google search will tell you that "to where" is not a grammatical phrase in English (nor has it ever been....the historical word for this is whither, but it was replaced by "where"). There only time you really ever see "to" and "where" next to each other is when "where" is the head of a following subordinate clause :)
Basically "where" acts like "here" and "there." "I am going to there" is simply wrong :)
I am a native English speaker, and I've been taught that "where are you running to" is improper, even if it is common for the layperson.
The point of duolingo is to get you to roughly translate the true meaning of a phrase and not to be literal. The meaning of this Turkish phrase would accurately be conveyed in English as "where are you running" so that answer should be accepted.
"To where are you running" is believed by many to be grammatically correct and it is at least grammatically acceptible, and it properly conveys the meaning of the Turkish phrase, so it should count as a correct answer as well.
The word "nereye" implies motion. The word "nerede" implies a static location. The word "running" is a verb of motion, so you would think it would always use "nereye," but as DottyEyes mentions below, "Where are you running?" can mean "In what location are you running?" (e.g., in the park, through the city, along the seashore, et alia). At least colloquially, however, it can mean "Where are you running to?" which is asking about the destination you'll end up at. So, while I am not crazy about sentences that end in prepositions, here it distinguishes itself enough so that you know to use "nereye" instead of "nerede" for this prompt.
"Where are you running to?" means "What is your destination while running?" Answers would be something like "To the train station" or "I'm running to to my friends' house."
"Where are you running?" would only be used if, for example, you knew the person was running for exercise, but you didn't know where exactly this was. Then you would say "Where are you running?" expecting an answer like "I'm running in the park tonight" or "I'm running at the school track today." These are not destinations; they are places where the running is happening.
I don't know if this is the normal Turkish way of asking someone where they typically run. An English conversation: Mary: You look so fit, Anna. How do you do it? Anna: I like to run. Mary: Where do you run? Anna: Usually in the park, but sometimes around the school track. So, Turk experts, in Turkish, could the boldface question be "Nerede koşuyorsun?"?
The rule about never ending a sentence with a preposition was exploded long ago, but some people still cling to it. https://www.merriam-webster.com/words-at-play/prepositions-ending-a-sentence-with