13.336. Coal delivered to the warehouse is intended for two plants. Coal delivery to the first plant started on June 1st at a rate of $m$ tons daily, including Sundays, and to the second plant - on June 8th at a rate of $n$ tons daily, including Sundays. By the end of June 16th, half of the initial amount of coal remained on the warehouse. On what date was all the coal removed from the warehouse, if both plants received an equal amount of coal?
Solution.

Let the total mass of coal be 1. Let $z$ be the number of days required to deliver half of all the coal to two plants simultaneously.

According to the condition, we have the system $\left\{\begin{array}{l}(8-1) m+(16-8+1)(n+m)=\frac{1}{2}, \\ z(n+m)=\frac{1}{2}, \\ (16+z) m=(16-8+1+z) n,\end{array}\right.$

from which $z=12$, and the entire coal was delivered by $16+12=28$ June.

Answer: June 28.