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

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,

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.

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