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.
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 email@example.com.