GeekDad Puzzle of the Week: A Highbrow Mathematics Puzzle

Geek Culture

And you tried to tell your high school algebra teacher there's no real-world use for math. Image: Flickr/ab9kt CC License

I have two dogs and two kids and all four of them fart. (My wife and I, of course, do not.) On a weekend morning, all four farters can frequently be found lounging in a small room with the door closed playing iPads, chewing things they shouldn’t, arguing about Star Wars and, well, you can guess what else they do. The gist is that the combined contribution of kids and dogs in this small, closed room creates a situation similar to the 1991 movie Backdraft in which the first non-farting person to open the door will be blown backwards and likely killed or at the very least blinded.

I think it’s funny to allow this person to be my wife, which I facilitate by precisely timing the phrase, “Hey, hon, can you tell the kids breakfast is ready?”

So here’s the question: When should I send in my wife to create maximum highbrow hilarity? The smell profile for each individual farter is detailed below (all times in minutes, when a smell passes below zero, consider it dissipated):

1. The Boy: Every five minutes with smell profile f(t):=-t^2+4t

2. The Girl: Every seven minutes with smell profile f(t)=-2t^2+5t

3. Old Labrador, Gus: Every six minutes with smell profile f(t)=-3t^2+10t

4. The Pup, Shaggy Chewbacca: Every three minutes with smell profile f(t)=-3t^2+4t+2

(The Pup may have rolled in something. Consider the final “+2” to be the baseline smell below which she cannot go, as is zero for the other three farters.)

Submit your answer to Geekdad Puzzle Central by Friday for your chance at a $50 ThinkGeek gift certificate!

[Editor’s note: you probably noticed already, but the variable in the equations should have been t and not x. That’s been fixed now.]

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