Little Suzy has a tricycle (you know, with three wheels). She wants to travel 1 mile with the tricycle, but she wants to spare her tyres (you know the price on tricycle tyres just keep going up). She is taking 2 spare tyres.

Assume she knows when to exchange wheels so that each of them travels an equal distance. How far does each wheel travel at the end of one mile? How did she exchange the wheels?

One solution would be that Little Suzy rode the tricycle 2/5 of a mile, then made her initial stop to replace with the two spares the two tires* on the wheels sharing an axle.
After proceeding another 1/5 mile, she made a second stop to replace the tire on the single wheel with one of the first removed tires.
After proceeding another 1/5 mile, before the last leg of the mile-long ride, she, again, replaced the tire on single wheel with the second of the two first removed tires.
At the end of the mile, each tire travelled 3/5 of a mile.

                1st     2nd     3rd
       Start    Stop    Stop    Stop    End        
Tire  1  :  2/5  +   0   +  1/5  +   0   =  3/5
Tire  2  :  2/5  +   0   +   0   +  1/5  =  3/5
Tire  3  :  2/5  +  1/5  +   0   +   0   =  3/5
Spare 1  :   0   +  1/5  +  1/5  +  1/5  =  3/5
Spare 2  :   0   +  1/5  +  1/5  +  1/5  =  3/5


*For those who do not know, the word 'tyre' is the British English spelling of the same word that in American English is 'tire', the usually inflated rubber ring that is fitted around a wheel.

Posted by Dej Mar on 2008-09-08 14:29:01