# 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?