Answers 307- PAT AND HIS PIG
The pig will run and be caught at 667) yards, and Pat will run 133YJ yards.
The curve of Pat's line is one of those curves the length of which may beexactly measured. It is 2 an2 I' where the pig's speed is assumed to be 1, and
n -
Pat runs n times as fast, and a is the initial distance between Pat and the pig.
- THE LADDER
The distance from the top of the ladder to the ground was ~ of the length
of the ladder. Multiply the distance from the wall-4 yards-by the denomi-
nator of this fraction-5-and you get 20. Now deduct the square of the
numerator from the square of the denominator of~, and you have 9, which
is the square of 3. Finally, divide 20 by 3, and there is the answer 67) yards.- A MA VPOLE PUZZLE
The height of the pole above ground must have been 50 ft. In the first case
it was broken at a distance of 29 ft. from the top, and in the second case
34 ft. from the top.- THE BELL ROPE
The bell rope must have been 32 ft. I ~ in. in length from ceiling to floor.- THE DISPATCH RIDER IN FLANDERS
Of course, a straight line from A to C would not be the quickest route. It
would be quicker to ride from A to E and then direct to C. The quickest pos-
sible route of all is that shown in the diagram on the following page by the
dotted line from A to G (exactly I mile from E) and then direct to C.
It is necessary that the sine of the angle FGC shall be double the sine of
AGH. In the first case the sine is 6 divided by the square root of 62 + 32 ,
which is 6 divided by the square root of 45, or the same as 2 divided by the