Tag Archives: travel puzzles

Clockwise Ant Puzzle

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This is actually a travel problem masquerading as a clock puzzle from Futility Closet.

“A problem by Argentinian puzzlist Jaime Poniachik, from the February 1992 issue of Games magazine:

An ant crawls onto a clock face at the 6 mark just as the minute hand is passing 12. She begins crawling counterclockwise around the face’s circumference at a uniform speed. When the minute hand passes her, she reverses course and crawls clockwise without changing her speed. Forty-five minutes after her first encounter with the minute hand, it passes her a second time and she departs. How much time did she spend on the clock face?”

Answer.

See Clockwise Ant Puzzle for solutions.

Ship and Seaplane Puzzle

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This is a puzzle from Boris Kordemsky’s 1972 Moscow Puzzles.

“A diesel ship leaves on a long voyage. When it is 180 miles from shore, a seaplane, whose speed is ten times that of the ship, is sent to deliver mail. How far from shore does the seaplane catch up with the ship?”

Answer.

See Ship and Seaplane Puzzle for solutions.

Yet Another Track Puzzle

This is another problem from Dan Griller.

“When Anthony and Benjamin run round a circular track in the same direction at constant but different speeds, they meet every 3 minutes.  When Benjamin changes direction (but maintains his speed) they meet every 40 seconds.

If Anthony is faster than Benjamin, calculate

(speed of Anthony) / (speed of Benjamin)”

Answer.

See Yet Another Track Puzzle for a solution.

Donkey Riding

This is a simple 1917 puzzle from Henry Dudeney.

“During a visit to the seaside Tommy and Evangeline insisted on having a donkey race over the mile course on the sands. Mr. Dobson and some of his friends whom he had met on the beach acted as judges, but, as the donkeys were familiar acquaintances and declined to part company the whole way, a dead heat was unavoidable. However, the judges, being stationed at different points on the course, which was marked off in quarter-miles, noted the following results:—The first three-quarters were run in six and three-quarter minutes, the first half-mile took the same time as the second half, and the third quarter was run in exactly the same time as the last quarter. From these results Mr. Dobson amused himself in discovering just how long it took those two donkeys to run the whole mile. Can you give the answer?

Answer.

See Donkey Riding for solutions.

Two Men Meet

This is another problem from the c.100AD Chinese mathematical work, Jiǔ zhāng suàn shù (The Nine Chapters on the Mathematical Art) found at the MAA Convergence website Convergence.

“A square walled city measures 10 li on each side.  At the center of each side is a gate.  Two persons start walking from the center of the city.  One walks out the south gate, the other the east gate.  The person walking south proceeds an unknown number of pu then turns northeast and continues past the corner of the city until they meet the eastward traveler.  The ratio of the speeds for the southward and eastward travelers is 5:3.  How many pu did each walk before they met? [1 li = 300 pu]”

Answer.

See Two Men Meet for a solution.

Railway Crossing Problem

This is an interesting problem from the 1966 Eureka magazine.

“A railway and a road run together for seven miles from P to Q. Two miles from P there is a level crossing, which is closed one minute before, and opened one minute after, a train passes.

A train passes a Stationary car at P and travels on to Q at 60 m.p.h., and, forgetting to slow down, crashes at Q; the car passes the train as it crashes. Assuming that stopping for an instant from full speed loses the car one minute, of what speed must it be capable?”

Answer

See the Railway Crossing Problem for a solution.

Unlawful Distance

This is a puzzle from the A+Click site.

“There is a fault with the cruise control on Hank’s car such that the speed continuously and linearly increases with time.  When he starts off the speed is set to exactly 60 mph.  He is driving on a long straight route with the radio on at full blast and he is not paying any attention to his speed.  After 3 hours he notices that his speed has now reached 80 mph.  For how many miles did he drive above the state speed limit of 70 mph?

Answer Choices:            125 miles     112.5 miles     105 miles     99.5 miles”

Answer.

See Unlawful Distance for solutions.

Another Passing Train Puzzle

This is another take on the passing train type puzzle from the Moscow Puzzles.

“A train moving 45 miles per hour meets and is passed by a train moving 36 miles per hour.  A passenger in the first train sees the second train take 6 seconds to pass him.  How long is the second train?”

Answer.

See Another Passing Train Puzzle for solutions.

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