An astronaut in a space craft looks out the window and sees an asteroid move pas a backward direction at 68 mph relative to the space craft. if the velocity of the space craft is 126 mph relative to the position of the sun, what is the velocity of the asteroid relative to the sun?

-194 mph

Explanation:

Taking into account the Sun as the center (origin, point zero) of the reference system, the velocity of the spacecraft relative to the Sun is:

 Note it is positive because the spacecraft is moving away from the Sun

Taking into account the spacecraft as the center of another reference system, the velocity of the asteroid relative to the spacecraft is:

Note it is negative because the asteroid is moving towards the spacracft.

Now, the velocity of the asteroid relative to the Sun is:

Finally:

This is the velocity of the asteroid relative to the Sun and its negative sign indicates it is moving towards the Sun.