The distance between Coco da Selva and Quixajuba is $24 \mathrm{~km}$. Two friends need to go from Quixajuba to Coco da Selva and a third friend needs to go from Coco da Selva to Quixajuba. They have a bicycle that is initially in Quixajuba. Each of them can walk at a speed of $6 \mathrm{~km} / \mathrm{h}$, or ride the bicycle at a speed of $18 \mathrm{~km} / \mathrm{h}$. Additionally, they can leave the bicycle at any point along the route.

![](https://cdn.mathpix.com/cropped/2024_05_01_9f6ce5ffa52bbf7500dfg-2.jpg?height=177&width=1012&top_left_y=2210&top_left_x=702)

Show how they can proceed to reach their destinations in no more than $2 \mathrm{~h} 40 \mathrm{~min}$.
We will call A and B the friends who are in Quixajuba and C the one who is in Coco da Selva. Our characters can follow the following strategy:

- In the first hour, A will ride a bicycle while B and C will walk. After this hour, A and C meet at kilometer 18 (measured from Quixajuba) and B is at kilometer 6.
- A continues walking and will reach his destination after one hour. Meanwhile, C continues on the bicycle and B stops to wait for C to arrive. Since the distance between C and B is 12 km, this will happen after 12/18 = 2/3 h, that is, 40 minutes.
- At this point, C passes the bicycle to B and each continues their journey, arriving at their destinations in one hour.

Thus, the total time spent by B and C was 2 h 40 min, while A spent 2 h.