Henry Ernest Dudeney/Modern Puzzles/29 - Timing the Motor-car/Solution
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Modern Puzzles by Henry Ernest Dudeney: $29$
- 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
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.
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Solutions: $29$. -- Timing the Motor-car
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $57$. Timing the Motor-car