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(A) Let $v_S$ and $v_P$ be the velocities of $S$ and $P$ waves respectively.Let $L$ be the distance between the epicenter and the seismograph.We have:

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$1920$

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(A) Let $v_S$ and $v_P$ be the velocities of $S$ and $P$ waves respectively.Let $L$ be the distance between the epicenter and the seismograph.We have:$L = v_S t_S \dots (i)$$L = v_P t_P \dots (ii)$Where $t_S$ and $t_P$ are the respective times taken by the $S$ and $P$ waves to reach the seismograph from the epicenter.Given:$v_P = 8 \; km/s$,$v_S = 4 \; km/s$From equations $(i)$ and $(ii)$:$v_S t_S = v_P t_P \implies 4 t_S = 8 t_P \implies t_S = 2 t_P \dots (iii)$It is given that the $P$ wave arrives $4 \; min$ before the $S$ wave:$t_S - t_P = 4 \; min = 240 \; s$Substituting $t_S = 2 t_P$ into the equation:$2 t_P - t_P = 240 \implies t_P = 240 \; s$Now,calculate the distance $L$ using equation $(ii)$:$L = v_P 	imes t_P = 8 \; km/s 	imes 240 \; s = 1920 \; km$Thus,the earthquake occurs at a distance of $1920 \; km$.

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