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)

Ram Mohith - 3 weeks, 3 days ago

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Thank you.

ilham syamsuddin - 3 weeks, 3 days ago

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But is my answer correct.

Ram Mohith - 3 weeks, 2 days ago

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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).

Brian Charlesworth - 3 weeks, 2 days ago

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@Brian Charlesworth Yes. That's unimaginable.

Ram Mohith - 3 weeks, 2 days ago

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