Page:Carroll - Tangled Tale.djvu/95

You say

"$\scriptstyle y\ =\ 6\ -\ {\frac {x\ -\ 3y}{6}}$, ....................................................................................................................................................................................................................................................

(i);

 

$\scriptstyle {\frac {x}{4{\frac {1}{2}}}}\ =\ 6$ ....................................................................................................................................................................................................................................................

(ii)."

I grant you (i), but I deny (ii): it rests on the assumption that to go part of the time at 3 miles an hour, and the rest at 6 miles an hour, comes to the same result as going the whole time at 4½ miles an hour. But this would only be true if the "part" were an exact half, i.e., if they went up hill for 3 hours, and down hill for the other 3: which they certainly did not do.

The sixteen, who are partially right, are Agnes Bailey, F. K., Fifee, G. E. B., H. P., Kit, M. E. T., Mysie, A Mother's Son, Nairam, A Redruthian, A Socialist, Spear Maiden, T. B. C., Vis Inertle, and Yak. Of these, F. K., Fifee, T. B. C., and Vis Inertle do not attempt the second part at all. F. K. and H. P. give no working. The rest make particular assumptions, such as that there was no level road—that there were 6 miles of level road—and so on, all leading to particular times being fixed for reaching the hill-top. The most curious assumption is that of Agnes Bailey, who says "Let $\scriptstyle x\ =$ number of hours occupied in ascent; then $\scriptstyle {\frac {x}{2}}\ =$ hours occupied in descent; and $\scriptstyle {\frac {4x}{3}}\ =$ hours occupied on the