You have to go to a star which is 395 light years away travelling at 142000 km/h. How many years does it take you?

Hello!

By definition, one light year is the distance which light (electromagnetic wave) travels in vacuum during one (Earth's) year. This distance does not depend on a wavelength of the light. Also, it does not depend on a frame of reference.

The speed of light in vacuum is about 300,000 km/s and one year is about `3.2*10^8` s. Therefore one light year is

`300,000` km/s * `3.2*10^8` s ≈ `9.5*10^13` km,

and 395 light years is about

`395*9.5*10^13` km ≈ `3.75 * 10^16` km.

There are about 8766 hours in a year. Our speed is supposed to be 142,000 km/h, which is the same as 142,000 * 8766 ≈ `1.24*10^9` (km/year).

Now we divide the distance in kilometers by the speed in kilometers per year and obtain the time:

`3.75 * 10^16` km  /   `1.24*10^9` km/year  ≈  `3.0 * 10^7` years.

This is the answer: about 30 millions years.