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

by : $46$

 * Baxter's Dog


 * This is an interesting companion to the "Man and Dog" puzzle.


 * 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?


 * My correspondent in Italy who sends me this is an exact man, and he says,
 * "Neglect the length of dog and time spent in turning."


 * I will merely add, neglect also the dog's name and the day of the month.

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.