Confusion in special relativity - total newbie

[iamaelephant]

I'm sure it's a stupid question but this is my first crack at SR so help would be great.

Homework Statement

Frame S' has a speed of 0.7c along the x axis relative to frame S. Clocks are adjusted so t=t'=0 at x=x'=0.

An even occurs in S at t1 = 3 x 10^7s at x1 = 40m. At what time does the event occur in S'?

Homework Equations

$$\beta = 0.7$$
$$\gamma = 1.4003$$
$$x' = \gamma (x - t\beta c)$$

The Attempt at a Solution

$$x' = \gamma (x - t\beta c) = (1.4003)(40 - (3 * 10^7)0.7 c) = -32.21m$$

Is this answer correct? It seems to me it can't possibly be right! What am I doing wrong?

 

[Shooting Star]

The Attempt at a Solution

$$x' = \gamma (x - t\beta c) = (1.4003)(40 - (3 * 10^7)0.7 c) = -32.21m$$

Is this answer correct? It seems to me it can't possibly be right! What am I doing wrong?

Why do you think this cannot be right? Think of where the origin of S' is wrt S when the event happens.

BTW, you have a direct formula for finding the time, which is the actual question.