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LOCOMOTION
AND SPEED PUZZLES.
"The race is not to the swift."—Ecclesiastes ix. II.
67.—AVERAGE
SPEED.
In a recent motor ride it was found that we had gone at the rate of ten miles
an hour, but we did the return journey over the same route, owing to the roads
being more clear of traffic, at fifteen miles an hour. What was our average
speed? Do not be too hasty in your answer to this simple little question, or it
is pretty certain that you will be wrong.
Solution
68.—THE
TWO TRAINS.
I put this little question to a stationmaster, and his correct answer was so
prompt that I am convinced there is no necessity to seek talented railway
officials in America or elsewhere.
Two trains start at the same time, one from London to Liverpool, the other
from Liverpool to London. If they arrive at their destinations one hour and four
hours respectively after passing one another, how much faster is one train
running than the other?
Solution
69.—THE
THREE VILLAGES.
I set out the other day to ride in a motor-car from Acrefield to Butterford,
but by mistake I took the road going via Cheesebury, which is nearer
Acrefield than Butterford, and is twelve miles to the left of the direct road I
should have travelled. After arriving at Butterford I found that I had gone
thirty-five miles. What are the three distances between these villages, each
being a whole number of miles? I may mention that the three roads are quite
straight.
Solution
70.—DRAWING
HER PENSION.
"Speaking of odd figures," said a gentleman who occupies some post in a
Government office, "one of the queerest characters I know is an old lame widow
who climbs up a hill every week to draw her pension at the village post office.
She crawls up at the rate of a mile and a half an hour and comes down at the
rate of four and a half miles an hour, so that it takes her just six hours to
make the double journey. Can any of you tell me how far it is from the bottom of
the hill to the top?"
Solution
71.—SIR
EDWYN DE TUDOR.
In the illustration we have a sketch of Sir Edwyn de Tudor going to rescue
his lady-love, the fair Isabella, who was held a captive by a neighbouring
wicked baron. Sir Edwyn calculated that if he rode fifteen miles an hour he
would arrive at the castle an hour too soon, while if he rode ten miles an hour
he would get there just an hour too late. Now, it was of the first importance
that he should arrive at the exact time appointed, in order that the rescue that
he had planned should be a success, and the time of the tryst was five o'clock,
when the captive lady would be taking her afternoon tea. The puzzle is to
discover exactly how far Sir Edwyn de Tudor had to ride.
Solution
72.—THE
HYDROPLANE QUESTION.
The inhabitants of Slocomb-on-Sea were greatly excited over the visit of a
certain flying man. All the town turned out to see the flight of the wonderful
hydroplane, and, of course, Dobson and his family were there. Master Tommy was
in good form, and informed his father that Englishmen made better airmen than
Scotsmen and
Irishmen because they are not so heavy. "How do you make that out?" asked Mr.
Dobson. "Well, you see," Tommy replied, "it is true that in Ireland there are
men of Cork and in Scotland men of Ayr, which is better still, but in England
there are lightermen." Unfortunately it had to be explained to Mrs. Dobson, and
this took the edge off the thing. The hydroplane flight was from Slocomb to the
neighbouring watering-place Poodleville—five miles distant. But there was a
strong wind, which so helped the airman that he made the outward journey in the
short time of ten minutes, though it took him an hour to get back to the
starting point at Slocomb, with the wind dead against him. Now, how long would
the ten miles have taken him if there had been a perfect calm? Of course, the
hydroplane's engine worked uniformly throughout.
Solution
73.—DONKEY
RIDING.
During a visit to the seaside Tommy and Evangeline insisted on having a
donkey race over the mile course on the sands. Mr. Dobson and some of his
friends whom he had met on the beach acted as judges, but, as the donkeys were
familiar acquaintances and declined to part company the whole way, a dead heat
was unavoidable. However, the judges, being stationed at different points on the
course, which was marked off in quarter-miles, noted the following results:—The
first three-quarters were run in six and three-quarter minutes, the first
half-mile took the same time as the second half, and the third quarter was run
in exactly the same time as the last quarter. From these results Mr. Dobson
amused himself in discovering just how long it took those two donkeys to run the
whole mile. Can you give the answer?
Solution
74.—THE
BASKET OF POTATOES.
A man had a basket containing fifty potatoes. He proposed to his son, as a
little recreation, that he should place these potatoes on the ground in a
straight line. The distance between the first and second potatoes was to be one
yard, between the second and third three yards, between the third and fourth
five yards, between the fourth and fifth seven yards, and so on—an increase of
two yards for every successive potato laid down. Then the boy was to pick them
up and put them in the basket one at a time, the basket being placed beside the
first potato. How far would the boy have to travel to accomplish the feat of
picking them all up? We will not consider the journey involved in placing the
potatoes, so that he starts from the basket with them all laid out.
Solution
75.—THE
PASSENGER'S FARE.
At first sight you would hardly think there was matter for dispute in the
question involved in the following little incident, yet it took the two persons
concerned some little time to come to an agreement. Mr. Smithers hired a
motor-car to take him from Addleford to Clinkerville and back again for £3. At
Bakenham, just midway, he picked up an acquaintance, Mr. Tompkins, and agreed to
take him on to Clinkerville and bring him back to Bakenham on the return
journey. How much should he have charged the passenger? That is the question.
What was a reasonable fare for Mr. Tompkins?
Solution
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