Answer
The new temporal coordinate of the event according to observer S' is 2.94 seconds.
Work Step by Step
When the observer moves in the opposite direction, it changes the sign of the velocity. We can use the given values in the Lorentz Transformation equations to solve for the new temporal coordinate of the event according to S'
$t'=\gamma (t-vx/c^2)$
$t'=1/\sqrt{1-\beta^2} (t-vx/c^2)$
$t'=1/\sqrt{1-0.400^2} (2.29s+0.400c*3.00*10^8/c^2)$
$t'=1/\sqrt{1-0.400^2} (2.29s+0.400*3.00*10^8/c)$
$t'=1/\sqrt{1-0.400^2} (2.29s+0.400*3.00*10^8/(299 792 458 m / s))$
$t'=2.94s$
