Amusements in Mathematics HTML version

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.
"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?"
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.
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