Calling all Math Nerds
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.
The tricky part is that there are varying speed limits. The first route (shown in red):
- A->B = 40 mph.
- No stop sign at B.
- B->C = 25 mph.
The second route (shown in blue):
- A->D = 30 mph.
- Stop sign at D.
- D->C = 30 mph.
Assuming I didn't miss any assumptions, which route of the two would be fastest?
Jake Munson
38 Yrs old
The average speed on the red route is higher, and has no stops.
At 45mph, 1 mile takes 90 seconds
At 30mph, 1 mile takes 120 seconds
At 25mph, 1 mile takes 144 seconds
AB + BC route = 117 seconds
Blue route = 120 seconds
The red route is shorter even before you factor in the blue stop.
Even if the acceleration factor is thrown in and makes any appreciable difference (it may decrease the time difference, but there would still be a difference), the red route will be faster.
If I were grading this problem on your math test, you'd get a C. The A+B side is 40 MPH, not 45. :)
and then you can take the A -> C route.
and btw, do you really do a complete stop at a stop sign? :D If not, then the lineup of how many cars at the stop sign means a lot more.
I could time it, but I thought it would be a fun problem to throw on my blog. :)
My question is so which side did you take and which side did your wife take? :)