Time Difference between two inertial frames of reference

[MEGA-DEEN]

Homework Statement

Let S and S' be two inertial frames of reference where S' is moving at a velocity of 0.6c relative to S.

When x = x' = 0, t = t' = 0, where t and t' are time of the clocks on S and S' respectively and x and x' are the x-coordinates of the S and S' frames respectively.

An event occurs at S when t = 2 × 10^-7s and x = 50m. What is t' when the event occurs at S'?

Homework Equations

t = ϒ t'

The Attempt at a Solution

Let t' be the proper time.
t = ϒ t' where t = 2 × 10^-7s and v = 0.6c.
Solving, I got t' = 1.6 × 10^-7s but the answer is 1.25 × 10^-7s.
What am I doing wrong?

 

[PeroK]

You've taken the wrong approach. The time an event takes place in S' depends on both the time and position it takes place in S.

Have you heard of the Lorentz Transformation?