Henry Ernest Dudeney/Modern Puzzles/35 - Sharing a Bicycle
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Modern Puzzles by Henry Ernest Dudeney: $35$
- 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,
- How are they to arrange the journey?
- Each man always either walks or rides at the speeds mentioned, without any rests.
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Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $35$. -- Sharing a Bicycle
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $63$. Sharing a Bicycle