Special Relativity: Time Dilation and the Twin Paradox

[the riddick25]

Homework Statement

there is a spaceship passing the Earth at a speed of 0.99c. if something takes 1 minute (according to the spaceship), how long does this take according to a clock on the earth.

and also, if something takes 3 minutes (according to the earth), how long will pass according to the spaceship

Homework Equations

Lorentz gamma factor
t=gamma x t'

The Attempt at a Solution

then i first did it, i worked out my gamma factor to be 7.088, which is corect.
when i did the first question, i found t to be 7.088 x 1 = 7.088 minutes

the second bit i am struggling with, firstly i thought it was going to be less, due to the fact the spaceship is moving, and therefore experiences time dialation. but now i am unsure.
if the person on the spaceship is in an inertial frame, it sees the Earth moving past at 0.99c, so it would see the event happen over a longer time like question 1.
could someone please help me with this, i know its probably that i haven't grasped something simple, but i would like to know

here are the two solutions, 0.42 mins if it is shorter, and 21.264 mins if it is the other.

i'm new to this forum, so sorry if i missed something

 

[Doc Al]

Both sets of observers see each other's clocks as running slow. Time dilation works both ways. If something takes 3 minutes according to an Earth clock, then the spaceship observers will say it took longer.

 

[the riddick25]

thanks a million :)