Question

Which ratios have a unit rate greater than 1? choose all that apply.
1/3 mile : 2 3/8 hours
9/8 miles : 5/6 hour
4 miles : 3 1/3 hours
9/5 miles : 3 hours
2 1/2 miles : 3 hours
7 miles : 3/4 hour

Answer 1

To determine which ratios have a unit rate greater than 1, we need to compute the unit rate for each ratio. The unit rate is found by dividing the distance by the time.

1. **1/3 mile : 2 3/8 hours**
- Convert 2 3/8 to an improper fraction: \(2 \frac{3}{8} = \frac{16}{8} + \frac{3}{8} = \frac{19}{8}\) hours
- Unit Rate = \(\frac{1/3}{19/8} = \frac{1/3 \times 8/19} = \frac{8}{57} \approx 0.14\)

2. **9/8 miles : 5/6 hour**
- Unit Rate = \(\frac{9/8}{5/6} = \frac{9/8 \times 6/5} = \frac{54}{40} = \frac{27}{20} = 1.35\)

3. **4 miles : 3 1/3 hours**
- Convert 3 1/3 to an improper fraction: \(3 \frac{1}{3} = \frac{10}{3}\) hours
- Unit Rate = \(\frac{4}{10/3} = \frac{4 \times 3}{10} = \frac{12}{10} = 1.2\)

4. **9/5 miles : 3 hours**
- Unit Rate = \(\frac{9/5}{3} = \frac{9/5}{3/1} = \frac{9}{15} = \frac{3}{5} = 0.6\)

5. **2 1/2 miles : 3 hours**
- Convert 2 1/2 to an improper fraction: \(2 \frac{1}{2} = \frac{5}{2}\) hours
- Unit Rate = \(\frac{5/2}{3} = \frac{5}{2} \times \frac{1}{3} = \frac{5}{6} \approx 0.83\)

6. **7 miles : 3/4 hour**
- Unit Rate = \(\frac{7}{3/4} = \frac{7 \times 4}{3} = \frac{28}{3} \approx 9.33\)

Now we summarize the unit rates:

1. \( \frac{8}{57} \approx 0.14\) (not greater than 1)
2. \( \frac{27}{20} = 1.35\) (greater than 1)
3. \( \frac{12}{10} = 1.2\) (greater than 1)
4. \( \frac{3}{5} = 0.6\) (not greater than 1)
5. \( \frac{5}{6} \approx 0.83\) (not greater than 1)
6. \( \frac{28}{3} \approx 9.33\) (greater than 1)

**Final List of Ratios with Unit Rates Greater than 1**:
- \( 9/8 \text{ miles : } 5/6 \text{ hour} \)
- \( 4 \text{ miles : } 3 1/3 \text{ hours} \)
- \( 7 \text{ miles : } 3/4 \text{ hour} \)