Answer:
[tex]\qquad \large \bold{Distance = 480 \: km} \\ [/tex]
Explanation:
Compute the distance of the epicenter from each of the stations using this formula:
[tex]\bold{Formula:}[/tex]
[tex]\quad \qquad \boxed{ \bold{ \: \: \: d = \frac{\:\:\:Td\:\:\:}{8 \: sec} \times 100 \: km \: \: \: }} \\[/tex]
[tex]\sf{where:}[/tex]
[tex]\quad\hookrightarrow\:\sf{d = distance \: (km)} \\[/tex]
[tex]\quad\hookrightarrow\:\sf{Td = time \: difference \: in \: the \: arrival \: time} \\ \sf{ of \: P-wave \: and \: S-wave \: (seconds)} \\[/tex]
This formula is suited because 8 seconds is the interval between the times of arrival of the P-wave and S-wave at a distance of 100 km.
[tex] \\ \underline{\mathcal{\blue{SOLUTION:}}}[/tex]
[tex]\qquad\sf\implies \: {d = \frac{ \: \: \: Td \: \: \: }{8 \: sec} \times 100 \: km} \\[/tex]
[tex]\qquad\sf\implies \: {d = \frac{ \: \: \: 38.4 \: sec \: \: \: }{8 \: sec} \times 100 \: km} \\[/tex]
[tex]\qquad\sf\implies \: {d = \frac{ \: \: \: 38.4 \: \cancel{sec} \: \: \: }{8 \: \cancel{sec}} \times 100 \: km} \\[/tex]
[tex]\qquad\sf\implies \: {d = 4.8 \times 100 \: km} \\ [/tex]
[tex]\qquad\sf\implies \: \underline{\boxed{\green{ \bold{{ \: \: \: d = 480 \: km \: \: \: }}}}} \\ [/tex]
[tex]\large \sf{Thus,} \\ [/tex]
[tex]\qquad\color{yellow}{\bigstar}\\\qquad \color{yellow}{ \bigstar} - \: \underline{ \boxed{\bold{ \green{ \: \: \: Distance = 480 \: km \: \: \: } }}} \: - \bigstar\\\qquad\color{yellow}{\bigstar}[/tex]