### Brain Teasers

# Rising Train Tracks

Henry is a new civil engineer, and is charged with planning the laying of a new type of ultra-rigid rails that expand only one inch per mile of length in temperature extremes. Henry's plan calls for the tracks (each of which is one mile in length) to be laid end-to-end with no gap between them, pinned to the ground at every other juncture, as shown below:

v_______ _______vv_______ _______v

Henry's boss sees the plan and says, "You fool! What about when the tracks expand?"

Henry replies, "The expansion will only be an inch over the whole mile length. If the tracks buckle, it will only be by an inch or two at most. The trains will certainly have no trouble bumping over these buckles."

Henry's boss says, "You're fired." Why was the boss so critical?

v_______ _______vv_______ _______v

Henry's boss sees the plan and says, "You fool! What about when the tracks expand?"

Henry replies, "The expansion will only be an inch over the whole mile length. If the tracks buckle, it will only be by an inch or two at most. The trains will certainly have no trouble bumping over these buckles."

Henry's boss says, "You're fired." Why was the boss so critical?

### Hint

Would Pythagoras have the same plan?### Answer

The rise in the middle of the tracks would have been much greater than Henry surmised. Using the Pythagorean Theorem, you will have a triangle with a base of one mile (or 63,360 inches), and a hypotenuse of one mile plus one inch (or 63,361 inches). To find the height, take the square root of (the square of the base minus the square of the hypotenuse). SQRT((63,361)^2 - (63,360)^2) = 355.98 inches, or over 29 feet!Hide Hint Show Hint Hide Answer Show Answer

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