Henry Ernest Dudeney/Modern Puzzles/35 - Sharing a Bicycle

by : $35$

 * Sharing a Bicycle


 * Two brothers had to go on a journey and arrive at the same time.
 * They had only a single bicycle, which they rode in turns, each rider leaving it in the hedge when he dismounted for the one walking behind to pick up,
 * and walking ahead himself, to be again overtaken.


 * What was the best way of arranging their distances?


 * As their walking and riding speeds were the same, it is extremely easy.
 * Simply divide the route into any even number of equal stages and drop the bicycle at every stage, using the cyclometer.
 * Each man would then walk half-way and ride half-way.


 * But here is a case that will require a little more thought.


 * Anderson and Brown have to go $20$ miles and arrive at exactly the same time.
 * They have only one bicycle.
 * Anderson can only walk $4$ miles an hour,
 * while Brown can walk $5$ miles an hour,
 * but Anderson can ride $10$ miles an hour to Brown's $8$ miles an hour.


 * How are they to arrange the journey?


 * Each man always either walks or rides at the speeds mentioned, without any rests.