To find out how long Yumi spent picking up litter, we need to solve the given equation:
[tex]\[
\frac{2}{x} = \frac{3}{x + 2}
\][/tex]
### Step-by-Step Solution:
1. Set up the Equation:
[tex]\[
\frac{2}{x} = \frac{3}{x + 2}
\][/tex]
2. Cross-Multiply to Eliminate the Fractions:
[tex]\[
2(x + 2) = 3x
\][/tex]
3. Distribute and Simplify:
[tex]\[
2x + 4 = 3x
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
4 = 3x - 2x
\][/tex]
[tex]\[
4 = x
\][/tex]
So, Juan spent [tex]\( x \)[/tex] hours picking up litter, which means Juan spent 4 hours.
5. Find How Long Yumi Spent Picking Up Litter:
Since Yumi took 2 hours longer than Juan:
[tex]\[
x + 2
\][/tex]
Substituting [tex]\( x = 4 \)[/tex]:
[tex]\[
4 + 2 = 6
\][/tex]
Therefore, Yumi spent [tex]\( 6 \)[/tex] hours picking up litter.
So, the correct answer is:
[tex]\[
\boxed{6 \text{ hours}}
\][/tex]
