Answer
$v=0.807c=2.42\times10^8m/s$
Work Step by Step
Solve for the speed from the time dilation relationship, equation 26–1a.
$$\Delta t_o = \Delta t \sqrt{1-\frac{ v^{2} } { c^{2} }} $$
$$v=c\sqrt{1-(\frac{\Delta t_o}{\Delta t})^2}$$
$$v=c\sqrt{1-(\frac{2.60\times 10^{-8}s}{4.40\times 10^{-8}s })^2}$$
$$v=0.807c=2.42\times10^8m/s$$