13.112. Two bodies move towards each other from two places, the distance between which is 390 km. The first body traveled 6 m in the first second, and in each subsequent second, it traveled 6 m more than in the previous one. The second body moved uniformly at a speed of $12 \mathrm{~m} / \mathrm{c}$ and started moving 5 seconds after the first. After how many seconds from the start of the first body will they meet?
## Solution.

Let $t$ s be the time of movement of the first body until the meeting; $t-5$ s of the second. The first traveled until the meeting $\frac{a t^{2}}{2}=\frac{6 t^{2}}{2}=3 t^{2}$ km; the second $12(t-5)$ km. According to the condition $3 t^{2}+12(t-5)=360$, from which $t=10$ s.

Answer: in $10 \mathrm{s}$.