Solution: The Cat’s Lasagna

The puzzle (from The mysterious temporal freeze) was:

A certain famous cat snarfs down an 11″x13″ pan of lasagna in 3 seconds flat. Assuming the fat feline has a bottomless pit for a stomach and continues to eat at the same rate, how long will it take him to devour a pasta the size of the state of Illinois?

Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterwards. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. Figure it out for yourself — and then check the answer just to prove that you got it right.


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Remember, don’t peek until you’ve given the problem a good workout on your own!
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Hint #1: There are 5,280 feet in a mile. Can you figure out how many square feet would be in a square mile?
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Hint #2: Have you tried using conversion factors?
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The Cat’s Lasagna

There are {5,280}^{2} = 27,878,400 square feet in a square mile. That’s a lot of pasta! Estimating one square foot of lasagna every 3 seconds, and using conversion factors to cancel out the units:

\frac{1\: sq.\: foot}{3\: sec.} \times \frac{1\: sq.\: mile}{27,878,400\: sq.\: feet} \times \frac{60\: sec.}{1\: min.} \times \frac{60\: min.}{1\: hour} \times \frac{24\: hour}{1\: day}

\times \frac{365.25\: day}{1\: year} \times \frac{100\: year}{1\: century}   = 37.7  square miles of lasagna per century.

I told you to round your answer to 2 significant figures, so why have I kept 3 figures here? To minimize round-off errors, I always like to keep one or two extra digits in my numbers until I get to the very end of the calculation.

If the area of Illinois is 55,584 square miles, then:

\left(55,584\: sq.\: miles \right) \times \frac{1\: century}{37.7\: sq.\: miles}   = about\: 1500\: centuries

To Put This in Perspective

Columbus discovered the New World 5 centuries ago. Jesus Christ lived 20 centuries ago. And about 46 centuries ago, the ancient Egyptians were building pyramids. To eat one pan of lasagna in 3 seconds sounds like a speed-eater to me, but it still would take an unimaginably long time to eat a pasta the size of just one mid-sized state.

Isn’t the world an amazing place?


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2 comments on “Solution: The Cat’s Lasagna

  1. Of course, he is capable of reproducing (with a little help at the beginning). If we went with the bad assumption that the number of fat cats doubled each year… but then we have more than units to play with.

    You know about cutting a piece of paper in half, and piling the halves on top of each other? Then doing it again. And again. And again… ?

    Like

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