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Answer:
d
=
s
t
Explanation:
distance = speed * time
here, the distance is from the earthquake centre to the seismic station.
both the P and S waves travel from the earthquake centre before being detected by the seismic station, so the distance is the same for both.
the speeds are given as
8740
m
/
s
for the P wave and
4100
m
/
s
for the S wave.
we also know that the P wave arrives
47.4
seconds before the S wave.
we do not know the time that the P wave takes to travel, but we can denote it as
t
P
.
the time that the S wave takes to travel can be denoted as
t
P
+
47.4
, where time is in seconds.
for the S wave, speed * time is
4100
⋅
(
t
P
+
47.4
)
for the P wave, speed * time is
8740
⋅
t
P
.
since the distances that they travel are the same, the two expressions for speed * time are equal.
4100
⋅
(
t
P
+
47.4
)
=
8740
⋅
t
P
if you expand the brackets, you can find that
4100
t
P
+
194340
=
8740
t
P
then you can subtract
4100
t
P
:
4640
t
P
=
194340
and divide by
4640
to find
t
P
, which is the time that P takes to travel:
t
P
=
41.883
...
seconds
since distance = speed * time, the distance that the P wave travels is
t
P
⋅
the speed of P.
this is
41.883
s
⋅
8740
m
/
s
, which gives
366057.42
m
.
in kilometres, this is
366
k
m
to
3
significant figures.