THE THREE RAILWAY STATIONS.
(
Patchwork Puzzles)
As I sat in a railway carriage I noticed at the other end of the
compartment a worthy squire, whom I knew by sight, engaged in
conversation with another passenger, who was evidently a friend of his.
"How far have you to drive to your place from the railway station?"
asked the stranger.
"Well," replied the squire, "if I get out at Appleford, it is just the
same distance as if I go to Bridgefield, another fifteen miles farther
on; and if I changed at Appleford and went thirteen miles from there to
Carterton, it would still be the same distance. You see, I am
equidistant from the three stations, so I get a good choice of trains."
Now I happened to know that Bridgefield is just fourteen miles from
Carterton, so I amused myself in working out the exact distance that the
squire had to drive home whichever station he got out at. What was the
distance?
Answer:
The three stations form a triangle, with sides 13, 14, and 15 miles.
Make the 14 side the base; then the height of the triangle is 12 and the
area 84. Multiply the three sides together and divide by four times the
area. The result is eight miles and one-eighth, the distance required.
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