294 Answers- THE RUSSIAN MOTORCYCLISTS
The two distances given were 15 miles and 6 miles. Now, all you need do
is to divide 15 by 6 and add 2, which gives us 41h. Now divide 15 by 4\6, and
the result (3YJ miles) is the required distance between the two points. This
pretty little rule applies to all such cases where the road forms a right-angled
triangle. A simple solution by algebra will show why that constant 2 is added.
We can prove the answer in this way. The three sides of the triangle are 15
miles, 9YJ miles (6 plus 3YJ miles) and 171) miles (to make it 21 miles each
way). Multiply by 3 to get rid of the fractions, and we have 45, 28, and 53.
Now, if the square of 45 (2,025) added to the square of 28 (784) equal the
square of 53 (2,809) then it is correct-and it will be found that they do so.
- THOSE RUSSIAN CYCLISTS AGAIN
The diagram gives all the correct distances. All the General had to do was
to square Pipipoff's 60 miles (3,600) and divide by twice the sum of that 60
and Sliponsky's 12 miles-that is, by 144. Doing it in his head, he, of course,
saw that this is the same as dividing 300 by 12, which at once gave him the
correct answer, 25 miles, as the distance from A to B. I need not show how all
the other distances are now easily obtained, if we want them.283. THE PRICE OF A GARDEN
The measurements given are absurd, and will not form a triangle. To do so
the two shorter sides must together be greater than the third. The Professor
gave it to his pupils just to test their alertness.