Light years are a measurement of distance just like anything else: they correspond to the distance that light travels in one year. So if light travels one light year in one year (by definition), then something moving at one tenth of speed of light will travel one light year in ten years.

But! It turns out that weird things can happen when you're traveling at near the speed of light. Say you were on a spaceship moving at one tenth the speed of light, and you're leaving Earth for some planet one light year away. I stay on Earth and watch you travel. Then indeed, from my perspective, it takes you ten years to get to that planet. But because you're moving at near the speed of light, it turns out that I see time passing more slowly for you than for me. That is, every time my watch ticks down a minute, I see a clock on your spaceship tick down a little less than one minute. That means that from your perspective (on the spaceship), it takes you less than ten years to get there! The difference in this case is pretty small: if you do out the math, it turns out that you feel it taking you about 99.4% of ten years. That means that you feel your trip as being about twenty days shorter than it seems to me.

This is a great and fascinating question! The answer might deceive you! Let’s start by a definition of light year. A light year is the distance that light travels in vacuum in one year, about 6 trillion miles or 10 trillion kilometers. One might therefore conclude that in order to travel one light year at one tenth the speed of light, this trip would take 10 years. This is correct, but is only half the answer!

The second half of the answer lies in the field of special relativity. The most relevant concept is called time dilation, and considers the frame of reference when we measure time. A simple idea is to think of two identical twins holding identical clocks, one on Earth and one traveling in a high-speed spaceship. The twin who travels and comes back will actually observe a shorter passage of time than the (now older) twin on Earth! This comes from the fundamental assumption that the speed of light must remain constant no matter which frame of reference is observed. In real life, satellites up in orbit have clocks that run slightly slower than the ones on the surface of the Earth.

So back to the puzzle: An observer on Earth sees a space traveler take 10 years to travel 1 light year at 1/10 the speed of light. But how much time passes for this space traveler? There is an equation for calculating time dilation given the relative velocity of an object:

Where Δ𝑡₀ is the traveler’s time frame (called proper time), Δ𝑡′ is Earth’s time frame, 𝑣 is the speed of the traveler (referenced by Earth), and 𝑐 is the speed of light. For everyday velocities (such as airplane speed), 𝑣 ≪ 𝑐 so the effects of time dilation are negligible. But greater than 1/10 the speed of light, we start to see noticeable effects.

If we plug the numbers into this equation, we see that the traveler actually observes a time span of Δ𝑡₀ = 9.95 years, or 18.3 days short of 10 years to complete the trip! In fact, if the traveler was going at 99% the speed of light (a supposed trip of just over a year), according to him, his trip would only take 52 days to complete!

These concepts of time dilation and special relativity are especially interesting to ponder. For instance, if one day we develop near-light-speed travel, we may be able to travel “forward” in time relative to Earth. A traveler could travel for a few years in her spaceship, and come back to Earth to find that everyone else has aged decades or centuries! Another possibility is that for those bold travelers that explore the deep reaches of space, they can travel great distances away without having aged much, all thanks to time dilation.

One last thing to consider, it is often confusing to figure out who is the observer in which reference. Just remember that Δ𝑡₀ is always the observer (can be person on Earth, space traveler, or anybody). From this, we know that 𝑣 must be the 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 velocity of the person or object being observed, whose time span is Δ𝑡′. This means that for two twins who are on Earth and traveling in space, each twin measures the other’s time to be going slower, because of the relative velocity between each other! A confusing idea indeed, but if we think about two twins observing each other from far away, each will observe the other as being physically smaller, but we know that both twins are of course the same size.

You may check out this page talking about time dilation and space travel:

You are correct: it would take ten years.

The speed of light has some weird properties: the closer you get to it, the slower time goes for you (but stays the same for everybody else). As a result, if you were traveling at almost the speed of light, then you could travel vast interstellar distances in mere hours as measured by the clock on your spacecraft, but for everybody else it would thousands of years. However, this effect is not significant if you are only going one tenth the speed of light.