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The simplest puzzles continue to give candidates the most trouble Most people have an intuitive reaction to the solution to this puzzle It would be wrong The following puzzle explores a very familiar theme but for some reason can be very perplexing
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Sally and John start off together on a one-mile walk to a nearby town John walks at a constant speed Sally s pace varies For the first half mile, Sally walks at one mile per hour faster than John For the second half mile, Sally walks one mile per hour slower than John What happened as they reached the nearby town Did they arrive at the same time, and if they didn t, who arrived first, Sally or John
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Hint: The math seems trivial Work it out The obvious answer is that Sally and John would arrive at the same time because the effects of Sally s variable speed exactly cancel each
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other out But in fact, no matter what Sally s speed is, John will always arrive first This is one candidate s reasoning that a recruiter found very compelling: When Sally walks one-half of the distance one mile slower than John, she loses more than she gains when she walks the other half of the distance one mile per hour faster than John For example, let s say that Sally s fast speed is three miles per hour, John s constant speed is two miles per hour, and Sally s slow speed is one mile per hour Sally will cover the first half mile in 10 minutes and the second half mile in 30 minutes However, John will cover the whole distance in only 30 minutes This is because when Sally is traveling fast for half a mile, John is traveling two-thirds as fast as she is, but when Sally is traveling slow for half a mile, she s only traveling one-half as fast as John Solution: The constant-speed walker (John) will always beat the variable-speed walker (Sally)
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96 HEADWIND, TAILWIND
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This is a deceptive problem similar in design to the previous puzzle Many recruiters select this puzzle when the candidate has arrived for the interview after taking a commercial airplane flight Candidates are quick to get this puzzle wrong precisely because so many of us take airplane trips for granted and think we understand the additive concepts of speed Recruiters look for candidates who really think the puzzle through and who reject the quick solution, even if they don t get the puzzle right at the end
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Consider a round-trip cross-country airplane flight, for example, from New York to Los Angeles and then back to New York How will a constant and uniform wind affect the total elapsed time of the flights relative to no wind Will a constant wind, uniform across both legs of the trip, make the total flight longer, make it shorter, or have no effect
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The obvious (and wrong) answer is to conclude that the effects of the headwind and tailwind will cancel each other out In fact, wind will always add delay to the total flight An understanding of the difference between an airplane s air speed and ground speed is useful Consider the following scenario: Suppose you have an airplane that flies 100 miles per hour relative to the ground You need to make a round-trip flight between city A and city B (200 miles) The goal is to make the trip in the shortest possible time Without a wind, the round-trip will take 4 hours Now let s imagine a uniform wind speed of 50 miles per hour The tailwind adds 50 miles per hour to the airplane s ground speed, resulting in the plane traveling at 150 miles per hour for the outbound leg of the round-trip It will take 1 hour and 20 minutes for the first leg The headwind subtracts 50 miles per hour from the speed of the airplane, resulting in a ground speed of 50 miles per hour It will take 4 hours for the inbound leg of the round-trip Going with the matching headwind and tailwind will cost us an extra hour and 20 minutes For a more rigorous proof of this somewhat startling result, consider this explanation: Let s w d plane s speed wind speed distance in one direction w 2)
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Wind will add time to the flight by the ratio (s 2)/(s 2 d/(s d/(s d/(s d/(s w) w) w) w) d/s d/(s d/(s d/s w) w)
time to complete leg flying with the wind time to complete leg flying against the wind round-trip time ratio of flying with wind to flying with no wind
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