Question

en has one rope that is 13 1 8 feet long and another that is 21 3 4 feet long. Kelsey has a rope that is 35 1 2 feet long. Which of the following shows who has more rope and how much more?
Jen has one rope that is 13 1 8 feet long and another that is 21 3 4 feet long. Kelsey has a rope that is 35 1 2 feet long. Which of the following shows who has more rope and how much more?

Answer 1

To determine who has more rope and how much more, let's first add the lengths of Jen's two ropes and then compare that to Kelsey's rope.

1. **Lengths of Jen's ropes**:
- Rope 1: 13 1/8 feet
- Rope 2: 21 3/4 feet

We need to convert 21 3/4 to a fraction with a denominator of 8 for easier addition:

\[
21 \frac{3}{4} = 21 \frac{6}{8} = \frac{21 \times 8 + 6}{8} = \frac{168 + 6}{8} = \frac{174}{8} = 21.75 \text{ feet}
\]

Now we can add the lengths of Jen's ropes:

\[
13 \frac{1}{8} + 21 \frac{3}{4} = 13 \frac{1}{8} + 21 \frac{6}{8} = 13 + 21 + \frac{1 + 6}{8} = 34 + \frac{7}{8} = 34 \frac{7}{8} \text{ feet}
\]

2. **Length of Kelsey's rope**:
- Kelsey's rope is 35 1/2 feet, or:
\[
35 \frac{1}{2} = 35 \frac{4}{8} = \frac{35 \times 8 + 4}{8} = \frac{280 + 4}{8} = \frac{284}{8} = 35.5 \text{ feet}
\]

3. **Comparison**:
- Jen's total rope length: \(34 \frac{7}{8}\) feet
- Kelsey's rope length: \(35 \frac{1}{2}\) feet

To compare, we can convert both lengths to improper fractions or decimals:
- \(34 \frac{7}{8} = 34.875\) feet
- \(35 \frac{1}{2} = 35.5\) feet

Now we subtract Jen's total length from Kelsey's:
\[
35.5 - 34.875 = 0.625 \text{ feet}
\]

This is equivalent to \( \frac{5}{8} \) feet.

**Conclusion**:
Kelsey has more rope than Jen. Kelsey has \( \frac{5}{8} \) feet more rope than Jen.