Kiran knits `2 (3)/(4)` pullovers in `14 (2)/(3)` hours and Anu knits `4 (1)/(2)` pullovers in `19 (1)/(2)` hours. Who is faster at knitting a pullover?

Answer

To determine who is faster at knitting a pullover between Kiran and Anu, we need to calculate the rate at which each person knits pullovers. We will find the number of pullovers knitted per hour for both Kiran and Anu.

### Step 1: Convert mixed numbers to improper fractions

**For Kiran:**
- Kiran knits \(2 \frac{3}{4}\) pullovers.
- Convert to improper fraction:
\[ 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \]

**For Anu:**
- Anu knits \(4 \frac{1}{2}\) pullovers.
- Convert to improper fraction:
\[ 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \]

### Step 2: Convert the total time taken to improper fractions

**For Kiran:**
- Kiran takes \(14 \frac{2}{3}\) hours.
- Convert to improper fraction:
\[ 14 \frac{2}{3} = \frac{14 \times 3 + 2}{3} = \frac{42 + 2}{3} = \frac{44}{3} \]

**For Anu:**
- Anu takes \(19 \frac{1}{2}\) hours.
- Convert to improper fraction:
\[ 19 \frac{1}{2} = \frac{19 \times 2 + 1}{2} = \frac{38 + 1}{2} = \frac{39}{2} \]

### Step 3: Calculate the rate of knitting pullovers per hour

**For Kiran:**
- Rate of Kiran:
\[ \text{Rate} = \frac{\text{Total pullovers}}{\text{Total time}} = \frac{\frac{11}{4}}{\frac{44}{3}} = \frac{11}{4} \times \frac{3}{44} = \frac{11 \times 3}{4 \times 44} = \frac{33}{176} = \frac{3}{16} \text{ pullovers per hour} \]

**For Anu:**
- Rate of Anu:
\[ \text{Rate} = \frac{\text{Total pullovers}}{\text{Total time}} = \frac{\frac{9}{2}}{\frac{39}{2}} = \frac{9}{2} \times \frac{2}{39} = \frac{9}{39} = \frac{3}{13} \text{ pullovers per hour} \]

### Step 4: Compare the rates

- Kiran's rate: \(\frac{3}{16}\) pullovers per hour
- Anu's rate: \(\frac{3}{13}\) pullovers per hour

To compare the two rates, we can find a common denominator or convert them to decimal values.

- Kiran's rate in decimal: \(\frac{3}{16} = 0.1875\)
- Anu's rate in decimal: \(\frac{3}{13} \approx 0.2308\)

### Conclusion

Since \(0.2308 > 0.1875\), Anu is faster at knitting pullovers than Kiran.

---