Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about , and that of the wave is . A seismograph records and waves from an earthquake. The first P wave arrives 4 min before the first wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?
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Let and have speeds of and , respectively. The and waves take and seconds to reach the position of the seismograph, respectively.