Problem 6.6. Ksyusha runs twice as fast as she walks (both speeds are constant).

On Tuesday, when she left home for school, she first walked, and then, when she realized she was running late, she started running. The distance she walked was twice the distance she ran. In the end, it took her exactly 30 minutes to get from home to school.

On Wednesday, Ksyusha left home even later, so she had to run twice the distance she walked. How many minutes did it take her to get from home to school on Wednesday?
# Answer: 24.

Solution. Let the distance from home to school be $3 S$, Ksyusha's walking speed be $v$, and her running speed be $-2 v$ (distance is measured in meters, and speed in meters per minute). Then on Tuesday, Ksyusha walked a distance of $2 S$ and ran a distance of $S$. And on Wednesday, she walked a distance of $S$ and ran a distance of $2 S$.

According to the condition, $30=\frac{2 S}{v}+\frac{S}{2 v}=\frac{4 S}{2 v}+\frac{S}{2 v}=\frac{5 S}{2 v}$, from which we get $\frac{S}{v}=30 \cdot \frac{2}{5}=12$.

Then on Wednesday, Ksyusha got to school in $\frac{2 S}{2 v}+\frac{S}{v}=\frac{S}{v}+\frac{S}{v}=12+12=24$ minutes.