Henry Ernest Dudeney/Modern Puzzles/29 - Timing the Motor-car/Solution

by : $29$

 * Timing the Motor-car

Solution

 * $21$ miles an hour.

Proof
Let $v$ be the speed of the motor-car.

Let $d$ be the distance to the corner from where the near-accident happened.

Let $t$ be the time it takes Pipkins to take $1$ step.

We have:


 * $v = \dfrac d {27 t}$

while Pipkins' speed gives:
 * $3 \tfrac 1 2 = \dfrac d {\paren {27 + 135} t}$

which leads us to:
 * $v = 6 \times 3 \tfrac 1 2$

and the answer.