Question

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?

Answer 1

Answer: It would take 10.16 million years.

Explanation:

Light travels at a speed $c=299 792 458\frac{m}{s}$.

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

$c\times(2.54million.years)=2.54million.light.years$

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

$v=\frac{c}{4}$ ⇒ $c=4v$

So, we have:

$4v\times(2.54million.years)=2.54million.light.years$

⇒ $v\times4(2.54million.years)=2.54million.light.years$

⇒ $v\times(10.16million.years)=2.54million.light.years$

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