Daily Math Puzzle: 2026-09-03
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2026-09-03
Two treasure hunters, Clara and Daniel, set out from a village (Point V) to retrieve an ancient coin from a ruin (Point R) 120 km away. Clara departs first, at 7:00 AM, traveling at a steady speed of 12 km/h. Daniel departs 3 hours later, at 10:00 AM, traveling faster at a steady speed of 20 km/h. Both hunters spend exactly 1 hour at the ruin (Point R) before turning around and returning to the village (Point V). At what distance from the village (Point V) will Clara and Daniel meet each other for the first time after Daniel has begun his return journey?
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Solution
120 km — Let's break down the timelines for Clara and Daniel:
**Clara's Journey:**
1. **Departure from V:** 7:00 AM
2. **Speed:** 12 km/h
3. **Distance to R:** 120 km
4. **Time to reach R:** 120 km / 12 km/h = 10 hours
5. **Arrival at R:** 7:00 AM + 10 hours = 5:00 PM
6. **Time spent at R:** 1 hour
7. **Departure from R (start of return journey):** 5:00 PM + 1 hour = 6:00 PM
**Daniel's Journey:**
1. **Departure from V:** 10:00 AM
2. **Speed:** 20 km/h
3. **Distance to R:** 120 km
4. **Time to reach R:** 120 km / 20 km/h = 6 hours
5. **Arrival at R:** 10:00 AM + 6 hours = 4:00 PM
6. **Time spent at R:** 1 hour
7. **Departure from R (start of return journey):** 4:00 PM + 1 hour = 5:00 PM
Now, let's analyze the meeting condition: "first time *after Daniel has begun his return journey*".
* Daniel begins his return journey at **5:00 PM**. At this moment, he is at Point R, which is 120 km from Point V.
* At **5:00 PM**, Clara *arrives* at Point R. She then spends an hour there.
Since both Clara and Daniel are simultaneously at Point R (120 km from Point V) at 5:00 PM (Daniel starting his return, Clara arriving), this constitutes their *first* meeting after Daniel has begun his return journey.
If one were to assume they must meet 'on the open road' while moving towards each other, Daniel (departing R at 5:00 PM at 20 km/h) is faster than Clara (departing R at 6:00 PM at 12 km/h) and leaves earlier. Therefore, Daniel will always be ahead of Clara on the return journey, and they would not meet again while both are actively moving back towards V. The trick lies in the precise definition of 'meet' and the exact timings at the ruin.
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