THE STAIRCASE RACE This is a rough sketch of the finish of
a race up a staircase in which three men took part. Ackworth, who is leading,
went up three steps at a time, as arranged; Barnden, the second man, the second
man, went four steps at a time, and Croft, who is last, went five a time.
Undoubtedly Ackworth wins. But the point is, how many steps are there in the
stairs, counting the top landing as a step? I have only shown the top of the
stairs. There may be scores, or hundreds, of steps below the line. It was not
necessary to draw them, as I only wanted to show the finish. But it is possible
to tell from the evidence the fewest possible steps in that staircase. Can you
do it?
TIMING THE CAR “I was walking along the road at three
and a half miles an hour,” said Mr. Pipkins , “ when the car dashed past me and
only missed me by a few inches.” “Do you know at what speed it was
going?” asked his friend. “Well, from the moment it passed me to
its disappearance round a corner I took
twenty-seven steps and walking on reached that corner with one hundred and
thirty-five steps more.” “Then, assuming that you walked, and
the car ran, each at a uniform rate, we can easily work out the speed.”
SHARING A BICYCLE Two brothers had to go on a
journey and arrive at same time. They had only a single bicycle, which they
rode in turns, each rider leaving it in the hedge when he dismounted for the
one walking behind to pick up, and walking ahead himself, to be again
overtaken. What was their best way of arranging their distances? As their
walking and riding speeds were the same, it is extremely easy. Simply divide
the route into any even number of
equal stages and drop the bicycle at every stage, using the cyclometer. Each
man would then walk half way and ride half way. But here is a case that will
require a little more thought. Anderson and Brown have to go twenty miles and
arrive at exactly the same time. They have only one bicycle.
How are they to arrange the journey? Each man always either walks or
rides at the speeds mentioned, without any rests? | |
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