Find lowest resonant frequence on this string

[Saladsamurai]

A string that is stretched between fixed supports separated by 75 cm has resonant frequencies of 420 and 315 Hz, with no resonant intermediate frequencies. What are (a) the lowest resonant frequency and (b) the wave speed?

Okay: So I know that since there are no intermediate resonant frequencies, then the two givens are of nth harmonic and nth+1 harmonic.

I also know that $$f_n=nf_1$$ and $$f_{n+1}=(n+1)f_1$$

so I need to find the fundamental frequency right? I am assuming this will involve 2 equations in 2 unknowns...

 

[Saladsamurai]

Should I use $$f_n=\frac{nv}{2L}$$ in a system of equations to solve for v and then plug that into find the 1st harmonic?...how bout I try it instead of asking?!