238 Answers- PICKLEMINSTER TO QUlCKVILLE
There are two possible distances that will fit the conditions-21O miles and
144 miles, only I barred the latter by the words, "at an ordinary rate." With
144 miles A would run 140 miles, while Band D ran 4 miles; so if the latter
went 2 miles per hour, the former would have to go 70 miles per hour-rates
which are certainly not "ordinary"! With 210 miles B and D go half the
speed of A, and C goes three-quarters the speed of A, so you can give them
reasonable rates.- THE DAMAGED ENGINE
The distance from Angiechester to Clinkerton must be 200 miles. The train
went 50 miles at 50 m.p.h. and 150 miles at 30 m.p.h. If the accident had oc-
curred 50 miles farther on, it would have gone 100 miles at 50 m.p.h. and
100 miles at 30 m.p.h.- THE PUZZLE OF THE RUNNERS
While Brown has only run ~ or 'Y.!4 of the course, Tompkins has run the re-
mainder %, less JA!, or 1~4. Therefore Tompkins's pace is IV-! times that of
Brown. Brown has now % of the course to run, whereas Tompkins has only ~.
Therefore Brown must go five times as fast as Tompkins, or increase his own
speed to five times I V-!, that is, s¥.I times as fast as he went at first. But the
question was not how many times as fast, but "how much faster," and S¥.I
times as fast is equal to s\I.i times faster than Brown's original speed. The cor-
rect answer is therefore 20\l.i times faster, though in practice probably im-
possible.
71. THE TWO SHIPS
The error lies in assuming that the average speeds are equal. They are not.
The first ship does a mile in VI2 hour outwards and in JA! hour homewards.
Half of the sum of these fractions is ¥.Is. Therefore the ship's average speed for
the 400 miles is a mile in ¥.Is hour. The average speed of the second ship is a
mile in YIO hour.