The cup of food required for a day, N=1/2 cup.
Total number of cups, T=26.
The number days 26 cups of food will last is,
[tex]\begin{gathered} n=\frac{T}{N} \\ n=\frac{26}{\frac{1}{2}} \\ n=26\times2=52 \end{gathered}[/tex]Therefore, 26 cups of food will last for 52 days.