8. Task by L. Carroll. Couriers from places $A$ and $B$ move towards each other uniformly, but at different speeds. After meeting, one needed another 16 hours, and the other needed another 9 hours to reach their destination. How much time does it take for each to travel the entire distance from $A$ to $B$?
8. Let $t$ be the time it took for the couriers to reach the meeting point, and $v_1$ and $v_2$ be the speeds of the couriers. Then $\left(v_{1}+v_{2}\right) t=v_{1}(16+t)=v_{2}(9+t) ; 16 v_{1}=v_{2} t$ and $v_{1} t=9 v_{2} ; \frac{16 v_{1}}{v_{1} t}=\frac{v_{2} t}{9 v_{2}}$ or $\frac{16}{t}=\frac{t}{9}$ and $t^{2}=16 \cdot 9$, from which $t=4 \cdot 3=12$ hours. Therefore, the first traveled to the destination for 28 hours, and the second for 21 hours.