An carthquake gencrates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The spced of $S$ waves is about $4.5 \,km / s$ and that of $P$ waves is about $8.0 \,km / s$. A scismograph records $P$ and $S$ wavcs from an carthquake. The first $P$ wave arrives $4.0\, min$ before the first $S$ wave. The cpicentre of the earthquake is located at a distance about