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?

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Comments

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 - 2 years, 2 months ago

Thank you.

Ilham Syamsuddin - 2 years, 2 months ago

But is my answer correct.

Ram Mohith - 2 years, 2 months 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).

Brian Charlesworth - 2 years, 2 months ago

@Brian Charlesworth – Yes. That's unimaginable.

Ram Mohith - 2 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$