How Does Speed Affect Time for a Bomb Threat on a Spaceship?

[jupiter13]

Homework Statement

In the far future, a spaceship is traveling from Earth to Saturn at 0.1c when it receives a terrorist threat. The crew learns that a bomb will go off in 3 hours. To prolong this time, the captain accelerates the ship to 0.7c. How long do they have to find the bomb now?

Homework Equations

\Deltat'=\gamma\Deltat

The Attempt at a Solution

By manipulating the equation, I solved for \Deltat'
3/\sqrt{1-(0.7)^2}= 4.2 hours

Where did I go wrong? Was the Lorentz transform done correctly?

 

[Doc Al]

Is the bomb and its timer on board the ship? Does increasing your speed change the rate at which your clock runs as far as you are concerned?

 

[jupiter13]

I can't believe I fell for that...but thank you very much fo your help!