20 Arithmetic & Algebraic Problemspassenger worked out from these facts the rate per hour at which each train
ran.
Can the reader discover the correct answer? Of course, each train ran with
a uniform velocity.68. PICKLEMINSTER TO QUICKVILLE
Two trains, A and B, leave Pickleminster for Quickville at the same time as
two trains, C and D, leave Quickville for Pickleminster. A passes C 120 miles
from Pickleminster and D 140 miles from Pickleminster. B passes C 126 miles
from Quickville and D half way between Pickleminster and Quickville. Now,
what is the distance from Pickleminster to Quickville? Every train runs uni-
formly at an ordinary rate.
- THE DAMAGED ENGINE
We were going by train from Anglechester to Clinkerton, and an hour
after starting an accident happened to the engine.
We had to continue the journey at three-fifths of the former speed. It made
us two hours late at Clinkerton, and the driver said that if only the accident
had happened fifty miles farther on the train would have arrived forty minutes
sooner. Can you tell from that statement just how far it is from Anglechester
to Clinkerton?
- THE PUZZLE OF THE RUNNERS
Two men ran a race round a circular course, going in opposite directions.
Brown was the best runner and gave Tompkins a start of one-eighth of the
distance. But Brown, with a contempt for his opponent, took things too easily
at the beginning, and when he had run one-sixth of his distance he met
Tompkins, and saw that his chance of winning the race was very small.
How much faster than he went before must Brown now run in order to tie
with his competitor? The puzzle is quite easy when once you have grasped its
simple conditions.
- THE TWO SHIPS
A correspondent asks the following question. Two ships sail from one port
to another-two hundred nautical miles-and return. The Mary Jane travels