Help: Question from Indonesian OSN Guru Matematika SD

I need help regarding this question this question is from 2019 Indonesian National Science Olympiade for Mathematics Teacher. The question is ...

Johnny and Diego are jogging on a circular track. Both start running at the same point. Johnny run with the speed of 50 km/h while Diego run with the speed of 80 km/h. after completing a lap, DIego rests for 30 minutes. After that he run again, and he meets Johnny. How long is the circumference of the track?

Note by Ilham Syamsuddin
3 weeks, 3 days ago

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I got the answer as $$\dfrac{200}{3} ~m$$. Here is my solution :

Let the circumference of the track be $$x$$. Also, lets assume that Diego takes time $$t$$ (in hours) to completer one lap. It is given that he takes $$0.5$$ hours rest and then meets Johny. From this we can conclude that Johny takes $$t + 0.5$$ hours to complete the lap. We know their speeds so put them in the condition $$x = v \cdot t$$ where, v is their respective speeds.

$x = 80 \cdot t \\ x = 50 \cdot (t + 0.5)$ On solving we get $$t = \dfrac56~hr= 50~min$$ and $$\boxed{x = \dfrac{200}{3}~km}$$.

(But I can't imagine a track which has circumference almost equal to 67 Km)

- 3 weeks, 3 days ago

Thank you.

- 3 weeks, 3 days ago

- 3 weeks, 2 days ago

I find the wording "After that he runs again, and he meets Johnny" confusing, but if it just means that Johnny finishes 30 minutes later than Diego then I get an answer of 200/3 km as well. This is an unusually long track, (10.61 km radius), and the speeds of the two runners is beyond what humans are capable of (without superpowers).

- 3 weeks, 2 days ago

Yes. That's unimaginable.

- 3 weeks, 2 days ago