1. A ball and a glove cost $1.10. The glove costs $1 more than the ball. How much does the ball cost?

2. Five golf ball machines produce five balls every five minutes. How long will it take 100 machines to make 100 golf balls?

3. Assume the earth is a perfect sphere. A ribbon is wrapped around the earth’s equator (about 24,000 miles). When you start to fit the two ends together you find the ribbon is one yard too long to fit nice and snug. If you distribute the slack evenly around the planet so that the ribbon hovers evenly above the surface all the way around, how far above the surface would the ribbon be?

The first two questions were taken from the book “David and Goliath” by Michael Gladwell. The third was taken from the book “This Explains Everything” by John Brockman.

Explanations

1. The answer seems to have to be the ball costs a dime. But if it did than the glove would cost $1.10 and the total cost would be $1.20. The right answer is the ball costs a nickel. And the glove cost $1.05. Total cost $1.10.

2. Again it just seems the answer must be 100 minutes. But remember each machine makes one ball every five minutes, so 100 machines will make 100 balls in five minutes.

3. This one seems really stupid — how can one yard even matter over such a large distance as 24,000 miles. The answer has to be that ribbon will only hover a very small fraction of an inch above the surface all the way around. The actual answer is the ribbon will have to be hovering almost one-half foot above the surface all the way around. Remember circumference equals Pi (or 3.14) times the diameter. So three feet of circumference adds almost a foot to the diameter.

This is also the reason we have more than one hole in which to buckle our belts. Beware … our intuition has limits.

Joe Concienne of Galveston, a chemical engineer who spent much of his career in Texas City, writes an occasional column on the basic concepts of science. He can be reached at concien@aol.com.

(17) comments

Joel Martin

Great article. I missed one and three.

Joe Concienne

Hoss: thanks for commenting

Steve Fouga

Enjoyed the article. Got 'em all. Engineering geek...

[cool]

Joe Concienne

Buckner: thanks for the feedback

George Croix

Not too hard.
Being a LMHS grad was not an encumbrance 45 years ago...

Carlos Ponce

LMHS at one time had the highest standards in the state of Texas.

Lars Faltskog

I only got #2 right. SCIENCE FAIL

Lars Faltskog

#3 was inplausable: If you started to wrap a ribbon around the earth, let's say at the Equator in Congo Africa going from west to east, then by the time you got to Kenya you would hit water (Indian Ocean). So then you would need to embark upon a ship and lay your ribbon on the water while you're on the ship, starting from Kenya. Ribbon might stay atop water only if the sea waves are smooth enough to keep ribbon intact. You might hit a little land again in New Guinea, but you still have to contend with the water again before you finish the job on the west coast of Ecuador.

Kevin Lang

OK. You have a point. How about if you go into your study and take the globe off the top shelf. Then, go up into your attic and pull out a roll of your holiday ribbon. Wrap it around the equator. Now, add a foot to it. You should have around 2" of slack around it. Unless you have enough people to help, you may have to just guess it.

Or, you could just do the math :-)
(or ask an 11th grade college prep student, or possibly some fifth graders!)

Lars Faltskog

Yes, I shall call upon 2 separate 11th graders and 2 separate 5th graders. One 11th grader - from a public school, the other from a charter or private school. Same for the 5th graders - one public, one private or charter. I can do a study to see which students answer the questions correctly - the ones from the charter or the public schooled ones?? Then, I can present the results to carlosrponce.

Paul Burgess

Where are the crossword puzzles?

Joe Concienne

Thanks for the comments. The only point I wanted to get across is that only logical thinking and doing the math consistently leads to correct answers. I've never had much luck using intuition in solving problems.

Comment deleted.
Joe Concienne

Kevjiang: you understood the whole intended concept of #3. I did not add the diameter to radius comment just to add a little last head scratch for purest like you.
Also you found the one possible flaw in #2, there is an implied assumption that all machines are identical. If they are not identical there is not enough info to get an answer.

George Croix

Do some more, please. I just got lucky on the first 3.
Don't give up on intuition ('gut feeling' in East Texas Pineywoods-ese).
There really are times when, if listened to, it will save your bacon...

Lars Faltskog

Sakes alive - Looks like someone got Comment Removed. Did someone try to slip in a math puzzle with "naughty" descriptions? OK, I can't resist -

"A flat-chested woman goes out shopping for a new bra. She goes into shop after shop asking if they have a size 28A but she can’t find one anywhere. Eventually she tries her luck in a small lingerie shop run by an old deaf lady. ‘Have you got anything in size 28A?’ asks the woman. ‘What was that, dear?’ says the old lady. The woman lifts up her T-shirt exposing her breasts and says, ‘Have you got anything for these?’ The old lady peers at the woman’s ta tas and says, ‘No, dear. Have you tried Clearasil?’"

from walksintoajoke.com

Kevin Lang

I think that was my comment that got removed. Not sure what I wrote that set off the "offensive" meters. As I recall, all I did was write about golf balls, diameters, and radii. If one can't talk about those in this forum, then I'll have to jump on the anti-PC bandwagon with gecroix, carlosrponce, JBG, Paul Hyatt, DottyOA, and the rest.

Once upon a time in these forums, if you ran afoul of the content judges, they would at least send you a note that explained what was offensive. Of course, that was when the site was all free. I don't think we ever really understood how valuable this site was when it was wide open to the trolls.

Lars Faltskog

Gosh, you're sooooooo offensive - LOL. One of our poster friends (who shall remain nameless) likes to point out my grammar flaws, so it's a wonder I haven't been given the boot.

Now, I do agree with Joe on all of this. It takes logic and mathematical aptitude beyond "basic math" to be successful at this kind of thing. Some people just "don't have it".

Interestingly, I thought about #2 regarding the machines perhaps not all producing at the same rate. Then again, I thought about the inability to be able to literally wrap a ribbon around the earth - the other prob. It is important to know that some folks (especially the young) will focus on the "inplausibles" rather than the math component of the problems. And/or, they'll focus on the situational aspects of word problems, EX from shmoop.com/word-problems/translating-words-examples.html:

"Lisa has five times as many books as she has CDs. She must be either over 45 or a librarian. Lisa also has 35 books. Okay, scratch that. She just hates music. How many CDs does she have?"

That word problem was written to help such literal folks grasp the concept a little better. If one extremely leans on the literary, he/she will have a harder time taking the challenge of word problems. I have to admit, back in college I was taken aback at how astronomy was wrought with physics and word problems (substitution), yet I was yearning to see films about how the earth will die someday, and I wanted to see visuals of the formations of black holes and white dwarves. I never got to see those visuals. I got turned off on astronomy ever since.

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