An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The speed of $S$ waves is about $4.5\,km/s$ and that of $P$ waves is about $8.0\, km/s$. A seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \,min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance about ..... $km$
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$\mathrm{t}_{\mathrm{s}}-\mathrm{t}_{\mathrm{p}}=4 \mathrm{\,min}$
$\frac{\mathrm{d}}{\mathrm{V}_{\mathrm{s}}}-\frac{\mathrm{d}}{\mathrm{V}_{\mathrm{p}}}=240 \mathrm{\,sec}$
$d\left[\frac{1}{4.5}-\frac{1}{8}\right]=240$
${\rm{d}} \simeq 2500\,{\rm{km}}$
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