In the not so distant future we can conceivably build a space ship that will travel 0.25 times the speed of light. how long would it take this ship to reach the andromeda galaxy?

It would take 10.16 million years.

Explanation:

Light travels at a speed .

A light-year is the distance that light travels in vacuum in one year.

The Andromeda Galaxy is 2.54 million light-years from the Earth.

This means that

Let's say is the speed of the ship. Then

⇒

So, we have:

⇒

⇒

So, at speed , it would need a time of 10.16 million years.