Henry Ernest Dudeney/Modern Puzzles/46 - Baxter's Dog/Solution

Modern Puzzles by Henry Ernest Dudeney: $46$

Baxter's Dog

Anderson set off from an hotel at San Remo at nine o'clock and had been walking an hour when Baxter went after him along the same road.

Baxter's dog started at the same time as his master and ran uniformly forwards and backwards between him and Anderson until the two men were together.

Anderson's speed is $2$, Baxter's $4$, and the dog's $10$ miles an hour.

How far had the dog run when Baxter overtook Anderson?

Solution

$10$ miles.

Proof

This is a variant on The Bulldozers and the Bee.

During the first hour, Anderson walks $2$ miles.

Baxter walks twice as fast, so catches up with Anderson after the latter has walked another $2$ miles, taking another hour to do so.

During that hour, the dog travels at $10$ miles an hour.

Thus the dog runs $10$ miles.

$\blacksquare$

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $46$. -- Baxter's Dog
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $74$. Baxter's Dog