by Dragon of Light » Sun Mar 30, 2008 6:38 pm
Consider the car and the space behind it as one "block".
Count how many "blocks" pass the Eye.
Each block has length [unparseable or potentially dangerous latex formula] km, where x is the speed in km/hr.
We can assume the speed is 15k, where k is an integer, because any speed between 15k and 15(k-1) produces blocks of the same size, yet more cars pass the Eye when the speed is faster.
The number of blocks that pass the Eye is [unparseable or potentially dangerous latex formula].
Substituting x=15k, we get [unparseable or potentially dangerous latex formula].
The limit as k approaches infinity of the equation is just [unparseable or potentially dangerous latex formula] or 3750.
It is true that the speed cannot be infinity. However, 3750 represents the number of blocks. It is possible for 3750 cars to pass the Eye at a finite speed, even though the space between the 3750th and 3751th car may not fully pass the Eye.
Thus our answer is 3750/10=375.
Record UIL/TMSCA scores:
Number Sense: 4 (2007 District UIL)
Calculator: 29 (2008 District UIL)
General Math: -30 (2008 TMSCA State)
Science: -81 (2007 TMSCA State)
CompSci: 7 (2008 District UIL)
I'm rather proud of my Calculator score. I broke 10.