A bicycle mishap

Puzzle

Here is another pretty bicycle puzzle which confronted Fred and his best girl on that same circuitous cross state tour which was to culminate at Erie. They had gone some distance when Fred's sprocket wheel broke off in such a way that temporary repairs were out of the question, and they were so remote from any hope of other assistance that it was deemed to be a mere question of reaching home in the shortest possible time.

The young lady could be depended upon to maintain a five-minute clip to the finish. Fred was an expert rider who could keep up a three- minute speed when riding upon his own wheel—but if he rode her wheel it reduced his speed to three and a half minutes. It was evident when the accident occurred that some walking must be done. She could walk a mile in twenty minutes, handicapped by leading a wheel. He could walk a 11 mile in fifteen minutes encumbered with the broken wheel. An extra sprocket wheel was at home and could be attached in ten minutes, so assuming they left home at 10 A. M. and returned at precisely 6 P. M., the problem is to tell how far they have travelled by their cyclometers, if they had gone as far away from home as was possible in accordance with the conditions described.

Solution

Answer

References

• Loyd, Sam [1914]. in Loyd, Sam, Jr.: Sam Loyd's Cyclopedia of 5000 Puzzles Tricks and Conundrums (in English). New York: Lamb Publishing company, page 11.