1. **Problem statement:** Demi and Maisy start moving towards each other from points $S$ and $T$ respectively. Maisy starts 1 hour after Demi and moves at double Demi's speed. When Demi has traveled $\frac{1}{6}$ of the distance between $S$ and $T$, Maisy has traveled the same distance. We need to find how many hours Demi takes to reach $T$. 2. **Define variables:** Let the total distance between $S$ and $T$ be $D$. Let Demi's speed be $v$ and Maisy's speed be $2v$. 3. **Time traveled by Demi when he covers $\frac{1}{6}D$:** $$ t_D = \frac{\frac{1}{6}D}{v} = \frac{D}{6v} $$ 4. **Maisy starts 1 hour later, so Maisy's travel time when Demi has traveled $\frac{1}{6}D$ is:** $$ t_M = t_D - 1 = \frac{D}{6v} - 1 $$ 5. **Distance Maisy travels in $t_M$ hours at speed $2v$ is:** $$ d_M = 2v \times t_M = 2v \left( \frac{D}{6v} - 1 \right) = \frac{2D}{6} - 2v = \frac{D}{3} - 2v $$ 6. **Given that Maisy has traveled the same distance as Demi at this time, so:** $$ d_M = \frac{1}{6}D $$ 7. **Set up the equation:** $$ \frac{D}{3} - 2v = \frac{1}{6}D $$ 8. **Solve for $v$:** $$ \frac{D}{3} - \frac{1}{6}D = 2v $$ $$ \frac{2D}{6} - \frac{1D}{6} = 2v $$ $$ \frac{1D}{6} = 2v $$ $$ v = \frac{D}{12} $$ 9. **Time for Demi to travel the whole distance $D$ at speed $v$ is:** $$ t = \frac{D}{v} = \frac{D}{\frac{D}{12}} = 12 $$ **Answer:** Demi takes 12 hours to reach point $T$.