Calling all Math Nerds

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Here’s a problem that is a real life question I’d like to solve. I don’t know if you could do this using ColdFusion (I know you don’t need to), but if you do use CF, you get extra credit. :)My wife and I have argued about which of two possible routes home is the quickest, and I figured some of the Math geniuses out there would be able to quickly solve this. The diagram below represents a part of my normal daily travels. I want to get from point A to C. I have the choice of taking the A->B->C route, or the A->D->C route. As you can see, all for sides of the square are 1/2 mile. Let’s also assume that I always start from a complete stop at point A, regardless of which route I choose, and I have to come to a complete stop at the end (point C), regardless of which route I choose.Math DiagramThe tricky part is that there are varying speed limits.The first route (shown in red):

  1. A->B = 40 mph.
  2. No stop sign at B.
  3. B->C = 25 mph.

Let’s assume that I can take the B corner at 8 miles an hour (no stop sign, and assuming that there are no cars coming that I’d have to stop for before making the turn).The second route (shown in blue):

  1. A->D = 30 mph.
  2. Stop sign at D.
  3. D->C = 30 mph.

Assuming I didn’t miss any assumptions, which route of the two would be fastest?