Catch the Train Riddle
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I drive at an average speed of 30 miles per hour to the railroad station each morning and catch my train. On a particular morning, there was a lot of traffic and at the halfway point, I had averaged only 15 miles per hour. How fast must I drive for the rest of the way to catch my train? 
Assuming that you usually reach the station on time to catch your train (i.e. with no time to spare) (because there is no mention of spare time in the question):
You won’t have been able to catch the train on that day however fast you drove the remaining distance!
Since your average speed was only half the required speed till you reached half-way. you will already have consumed the entire time required (at usual speed) to reach the station. By that time, the train would have reached the station. Time remaining till the train arrives is ZERO. No amount of fast driving will take you to the station in zero time. You missed the train.
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