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For The Mathematically Inclined

Anil Saigal
02/01/2010

PROBLEM # 1
The front wheels of a wagon measure 3.5 feet in diameter. The real wheels measure 4.25 feet in diameter. While the wagon is stopped somebody makes a chalk mark on both a front and rear wheel. How far must the wagon travel before both chalks marks return to their initial position at the same time?

PROBLEM #2

There is a 6 foot wide alley. Both walls of the alley are perpendicular to the ground. Two ladders, one 10 feet long, the other 12 feet, are propped up from opposite corners to the adjacent wall, forming an X shape. All four feet of each ladder are firmly touching either the corner or the wall. The two ladders are also touching each other at the intersection of the X shape. What is the distance from the point of intersection to the ground?

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-020410 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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Problems from 01/21/10

PROBLEM # 1

A rectangle has length 10 feet and width 7 feet. What is the area of largest circle that can fit in this rectangle?

SOLUTION

38.48


PROBLEM #2

Four dogs occupy the four corners of a square with side of length 10 feet. At the same time each dog starts walking at the same speed directly toward the dog on his left. Eventually all four dogs will converge at the center of the square. What is the distance each dog walks until he reaches the center?

SOLUTION

10

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Congratulations to Sitaram Chandawarkar who was the winner of the last set of puzzles.



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