Genius of the MonthTM Runners-Up - 10/8/06
Sam's victory in Friday's Genius of the MonthTM contest in no way detracts from the valiant efforts of several other math almost-geniuses-of-the-month out there. The following people also responded with correct answers within 10 hours of the post going up... or in some cases, within 5 minutes of getting to work and starting to waste corporate America's time.

2nd Place - Ryan Pastrovich
3rd Place - Brian Saito (though one might argue that Pastro only nudged him out because he was 2 timezones ahead)
4th Place - Jeff Henderson
5th Place - Sean Verde
6th Place - Jeremy Abramson (gets the yellow participation ribbon, since he offered only an answer and no explanation... which is also VERY uncharacteristic of Jeremy)

Where are all the girls at? The fact that only guys responded to this post leads me to only two possible explanations:
A) Women can't do math
B) No women read my site anymore, as I've offended all of them with comments like A)

Their explanations:

RYAN:
30/45 = 2/3, so she spent 3/2 of the time driving 30 mph that she did going 45. Throw that into 60 minutes, and you get 36/24. So she went 18 miles each way. Given that her name is Esther, she was probably sitting on three phone books to see over the steering wheel, which adds weight to the car, which decreases her miles per gallon, which pollutes the environment more, and kills a giant sequoia 10 minutes earlier than expected, which causes the hippie chained to the tree fall and die, which leads to some environmental terrorist SuperHippie blow up an SUV dealership, which causes us to bomb Saudi Arabia because we thought some Muslims did it, which causes them to bomb Isreal, who bombs Russia for giving the terrorists the bombs, which bombs us because Ben Affleck was asleep at the time and could not convince them that it wasn't us, which kills Esther. Thus, tomorrow she will drive zero miles to work.

BRIAN
The answer is 18 Miles.
Why this makes me a "genius" I don't know. It's a simple system of equations, as long as you remember that (rate)(time)=distance.
T1 = time to get to work
T2 = time to get home
Morning: (45M/H)*(T1) = D
Evening: (30M/H)*(T2) = D
Time relationship: T1+T2 = 1Hour -> T1 = 1H -T2
Substitute this into Morning equation: (45M/H)*(1H-T2) = D from the evening equation we know that (45M/H)*(1H-T2) = (30M/H)*(T2) Simple Algebra... T2 = 0.6Hours. Knowing this we can sub back into Evening equation and (30)*(0.6) = 18
I'd like to point out that this bitch Esther lives nowhere near me. I wish I could go 30MPH on the 405 leaving from work. That would be "Ludicrous Speed"... Holler at these Hoes.

JEFF HENDERSON gets the award for Simplest Answer: 18 miles?
Ester drove to work 1.5x as fast in the morning than she did in the evening, so the amount of time spent in the car in the evening divided by the amount of time spent in the car in the morning = 1.5. 36/24 is the only combination adding to 60 that = 1.5.
If Esther spent 24 minutes in the car in the morning (=.4 hours) * 45 mph = 18. Likewise, if she spent 36 minutes in the car in the evening (=.6 hrs) * 30 mph = 18.

Of course, his question mark at the beginngin also gets him the Doing-Math-Like-a-Pussy award for not saying it with conviction.

SEANN VERDE, as usual, gets the award for the strangest answer:
Esther drove 18 miles to work in the morning. This is a simple Law of Averages problem. Explanation:
Esther is clearly in her eighties, as no one in their right mind in the latter three-quarters of the 20th century would name their child Esther.
Since old people always have to stay within a 19-mile radius of a hospital (unless she has HomeAlert(R), but since the problem doesn't mention it, we can assume she doesn't), and the average old person lives 2.5 miles from the nearest hospital, we can deduce that her workplace must be no more than 19 + 2.5 = 21.5 miles from her house, so a maximum total round trip of 43 miles.
Now, old people smell funny, but more relevantly, they have to "take care of their business" a lot. Using the Law of Grannies, we find (60, baseage) + (20, number of years above 60)* (1, number of hours) / (40, Foley's Constant) = 2 bathroom stops during the trip.
Since Esther managed to maintain an average speed of at least 30mph, and she must have stopped to use the bathroom at least twice, her actual velocity was as follows:
((60min, total trip time) - ((20min stop)*2)) = 20min, actual travel time (2*30*45)/(30+45)) = 36mph, observed average mph [HINT]
So she would have had to travel three times as fast as 36, giving us 108 mph.
Converting to furlongs, we have 864 furlongs/hour, which is pretty fast.
Slow down Esther. And remember, seatbelts save lives!!
All right, we're almost done. Eight Hundred Sixty Four furlongs/hour actual speed. Forty Three maximum miles. One Granny. You do the math.
Or I will. 864/ (2, average number of dead children at age eighty) = 432. 432/43 ~ 10 max furlong/mile-hours. Factoring out furlongs and hours, taking into account the Muumuu-Drag-Effect, and remembering the age at which we are allowed to vote, we get 18, also the age at which U.S. house representatives are no longer sexually interested in you.
Esther drives 18 miles. Each way. Every day. Two of her children are dead. And she has to use the bathroom twice an hour. Someone should do Esther a favor.
-S

Did we really expect less from Verde?

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