Henry Ernest Dudeney/Modern Puzzles/45 - The Man and the Dog

Modern Puzzles by Henry Ernest Dudeney: $45$

The Man and the Dog

"Yes, when I take my dog for a walk," said a mathematical friend, "he frequently supplies me with some interesting problem to solve.

One day, for example, he waited, as I left the door, to see which way I should go,

and when I started he raced to the end of the road, immediately returning to me;

again racing to the end of the road and again returning.

He did this four times in all, at a uniform speed,

then ran at my side the remaining distance, which according to my paces measured $27$ yards.

I afterwards measured the distance from my door to the end of the road and found it to be $625$ feet.

Now, if I walk $4$ miles per hour, what is the speed of my dog when racing to and fro?"

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $45$. -- The Man and the Dog
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $73$. The Man and the Dog