Page:Carroll - Tangled Tale.djvu/94

78 Twenty-seven answers have come in. Of these, 9 are right, 16 partially right, and 2 wrong. The 16 give the distance correctly, but they have failed to grasp the fact that the top of the hill might have been reached at any moment between 6 o'clock and 7.

The two wrong answers are from and. The former makes the distance "23 miles," while her revolutionary companion puts it at "27." says "they had to go 4 miles along the plain, and got to the foot of the hill at 4 o'clock." They might have done so, I grant; but you have no ground for saying they did so. "It was 7½ miles to the top of the hill, and they reached that at ¼ before 7 o'clock." Here you go wrong in your arithmetic, and I must, however reluctantly, bid you farewell. 7½ miles, at 3 miles an hour, would not require 2¾ hours. says "Let $$\scriptstyle x$$ denote the whole number of miles; $$\scriptstyle y$$ the number of hours to hill-top; ∴ $$\scriptstyle 3y\ =$$ number of miles to hill-top, and $$\scriptstyle x\ -\ 3y\ =$$ number of miles on the other side." You bewilder me. The other side of what? "Of the hill," you say. But then, how did they get home again? However, to accommodate your views we will build a new hostelry at the foot of the hill on the opposite side, and also assume (what I grant you is possible, though it is not necessarily true) that there was no level road at all. Even then you go wrong.