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

by : $29$

 * Timing the Motor-car
 * "I was walking along the road at $3 \tfrac 1 2$ miles an hour," said Mr. Pipkins,
 * "when the motor-car dashed past me and only missed me by a few inches."


 * "Do you know what speed it was going?" asked his friend.


 * "Well, from the moment it passed me to its disappearance round a corner I took $27$ steps, and walking on reached that corner with $135$ steps more."


 * "Then, assuming you walked, and the car ran, each at a uniform rate, we can easily work out the speed."

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.