1. **Stating the problem:** A knight must arrive at exactly 17h00. Traveling at 15 km/h makes him arrive 1 hour early, and at 10 km/h makes him arrive 1 hour late. We need to find: - The departure time - The distance traveled - The actual speed he traveled 2. **Define variables:** Let $d$ be the distance in km. Let $t$ be the time in hours it takes to arrive exactly at 17h00. 3. **Set up equations:** If traveling at 15 km/h, he arrives 1 hour early, so travel time is $t - 1$ hours: $$ d = 15(t - 1) $$ If traveling at 10 km/h, he arrives 1 hour late, so travel time is $t + 1$ hours: $$ d = 10(t + 1) $$ 4. **Equate the distances:** Since distance $d$ is the same: $$ 15(t - 1) = 10(t + 1) $$ 5. **Solve for $t$:** $$ 15t - 15 = 10t + 10 $$ $$ 15t - 10t = 10 + 15 $$ $$ 5t = 25 $$ $$ t = 5 $$ 6. **Calculate distance $d$:** Using $d = 15(t - 1)$: $$ d = 15(5 - 1) = 15 \times 4 = 60 $$ km 7. **Calculate actual speed:** Speed $v = \frac{d}{t} = \frac{60}{5} = 12$ km/h 8. **Calculate departure time:** He must arrive at 17h00 after traveling for 5 hours, so: $$ \text{Departure time} = 17:00 - 5 \text{ hours} = 12:00 $$ **Final answers:** - Departure time: 12:00 - Distance traveled: 60 km - Actual speed: 12 km/h