Calculate distance from expolision - Waves

[Jason17]

Homework Statement

A recording station observed that there was an interval of 68s between the reception of P (push or primary) waves and S (shake or secondary waves) from an underground nuclear test explosion.
The speed of P and S waves in the Earths crust are 7800 ms^-1 and 4200 ms^-1, respectively.

Calculate the distance of the test site from the explosion

Homework Equations

Speed = Frequency x wavelength (v=fλ)
Speed of electromagnetic radiation = 3 x 10^8 ms^-1
Speed of sound in air 340 ms^-1
Speed of sound in water and sea water = 1500 ms^-1

The Attempt at a Solution

So I am using this formula:
Speed = Frequency x wavelength (v=fλ)
I have the speed, 7800 & 4200 and its frequency i believe? is 68 seconds

Im trying to find the distance (is this the wavelength?)
Wavelength= Speed/Frequency

The answer is 620 km. Which i cannot get to :\

Help appreciated, ty in advance

 

[nasu]

You don't really need any of the formulas that you wrote.
You know the speed already.
68s is not frequency but the time difference between the detection of the two waves.

Just use the equation for motion with constant speed for each one of the waves.

 

[Jason17]

sorry, i don't understand what your trying to say.

Equation of motion?
S=u.t + 0.5.a.t^2 ?
or
S=(u+v)/2 . t?

I still can't get to 620km :(

 

[nasu]

No, the wave has constant speed.
So it's just
d=u1*t1
and
d=u2*t2

where d is the distance between source and receptor and t1, t2 are the propagation times for the two waves.
You don't know t1 and t2 but you know the difference, t1-t2=68 s.
Can you solve the problem now? You need to find d.