Doppler Effect Source Moving Away

[JSGandora]

Homework Statement

Superman has a blue light of wavelength 480nm. How fast must he fly away from you so that his light appears orange, with a wavelength of 600nm?

Homework Equations

f'=\frac{f}{\left(1+\frac{v_s}{v}\right)}
and
f=\frac{c}{\lambda}

The Attempt at a Solution

I used the equation f'=\frac{f}{\left(1+\frac{v_s}{v}\right)} and solved for v_s and got my answer to be 75\times 10^8 m/s but the answer key said 57.0\times10^6 - 67\times10^6m/s. What did I do wrong?

 

[JSGandora]

Someone told me that the equation \lambda =\lambda_{0}\sqrt{{1-\beta}\over{1+\beta}} give the correct answer (like the other thread). Why didn't the usual doppler effect equation work here? I'm confused.