I'm a long time visior of the forums, but have never had anything "post" worhy before. So, I finally registered today. Just before Holiday break, our Teacher dropped a fun problem for us to figure out, and I wanted to share it. She asked us to break down and solve the following, not for a grade or extra credit--it was more like a dare.
"1 direction on the interstate. 2 lanes traveling in that direction. 1 constant vehicle (control). 1 inconsistent vehicle or unknown variable. Divided by 3 known variables, representing obstacles."
She asked us to figure the ratio of the control car, avoiding the 3 obstacles. And, figure the ratio of the X variable vehicle, avoiding the same 3 obstacles.
Edit: Clarification/Examples - you create the rules of the control. Since, she used the interstate as an example, I used common interstate laws - Moving to the right lane, allowing faster traffic to pass, moving to the left lane to make room for merging interstate traffic, obstructing traffic, no drastic speed reductions, and a speed limit of 65MPH. The control vehicle can never break these laws, in contrast to the x variable vehicle that can.
This is how I started to break down the problem.
Scenario begins with the control vehicle in the left lane, with the x variable vehicle, approaching from behind.
Examples of 3 known obstacles -
1. Right lane merging interstate traffic, from a ramp.
2. The possibility of the control vehicle or x vehicle becoming an obstacle to the other (does not include other vehicles).
3. Consistent traffic behind the control vehicle and the X vehicle - the situation where the control vehicle or X vehicle actually become the obstacle to other drivers (control vehicle would be aware of this possibility, which defines it as a known obstacle.
Feel free to use my examples to figure the problem. I enjoyed it and I'm looking forward to seeing what you came up with. If you have any questions, please PM or post on this thread.