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Question
The front wheels of a wagon are 11 feet in circumference and rear wheels are 13 feet. One spoke in each wheel is painted red. When the wagon starts on a trip, all of the red spokes are upright and above the axle.  When the wagon stops, all of the red spokes are upright again for the 533rd time.  Calculate distance(in miles)traveled by the wagon.

Thanks.

Answer
"The front wheels of a wagon are 11 feet in circumference and rear wheels are 13 feet."
11 and 13 are prime numbers, so their least common multiple is 1113 = 143.
The red spokes are realigned when the wagon has traveled 143 feet.

"When the wagon stops, all of the red spokes are upright again for the 533rd time."
533143 = 76,219
The wagon has traveled 76,219 feet.

1 mile = 5280 feet
76,219 ft 1 mile/(5280 ft) ≅ 14.44 miles

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Janet Yang

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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