Question

a spaceship traveled 1/2 of a light-year from earth to planet x and 1/3 of a light-year from planet x to planet y. then it traveled 1/3 of a light-year from planet y back to earth. how many light - years did the spaceship travel in all?
light - years

Explanation:

Step1: Identify the distances traveled

The spaceship traveled three segments: from Earth to Planet X: $\frac{1}{2}$ light - year, from Planet X to Planet Y: $\frac{1}{3}$ light - year, and from Planet Y back to Earth: $\frac{1}{3}$ light - year.

Step2: Sum the distances

To find the total distance, we add these three fractions together. The formula for the total distance $d$ is $d=\frac{1}{2}+\frac{1}{3}+\frac{1}{3}$. First, we add the two $\frac{1}{3}$ terms: $\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$. Then we add $\frac{1}{2}$ to $\frac{2}{3}$. To add these two fractions, we find a common denominator, which is 6. So $\frac{1}{2}=\frac{3}{6}$ and $\frac{2}{3}=\frac{4}{6}$. Then $\frac{3}{6}+\frac{4}{6}=\frac{3 + 4}{6}=\frac{7}{6}$.

Answer:

$\frac{7}{6}$