Suman covers `2 (4)/(5)` km in `(7)/(12)` hours.
a. How much time is required to cover `6 (1)/(5)` km?

Answer

To solve the problem step by step, we need to find out how much time Suman requires to cover `6 (1)/(5)` km, given that she covers `2 (4)/(5)` km in `(7)/(12)` hours.

### Step 1: Convert the mixed numbers to improper fractions
1. Convert `2 (4)/(5)` km to an improper fraction:
- \( 2 \frac{4}{5} = 2 \times 5 + 4 = 10 + 4 = \frac{14}{5} \) km

2. Convert `6 (1)/(5)` km to an improper fraction:
- \( 6 \frac{1}{5} = 6 \times 5 + 1 = 30 + 1 = \frac{31}{5} \) km

### Step 2: Calculate Suman's speed
3. Suman covers `\(\frac{14}{5}\)` km in `\(\frac{7}{12}\)` hours. To find her speed:
- Speed = Distance / Time
- Speed = \( \frac{14/5}{7/12} \)
- To divide by a fraction, multiply by its reciprocal:
- Speed = \( \frac{14}{5} \times \frac{12}{7} \)
- Speed = \( \frac{14 \times 12}{5 \times 7} = \frac{168}{35} = \frac{24}{5} \) km/h

### Step 3: Calculate the time required to cover `6 (1)/(5)` km
4. Now, we need to find the time required to cover `\(\frac{31}{5}\)` km:
- Time = Distance / Speed
- Time = \( \frac{31/5}{24/5} \)
- To divide by a fraction, multiply by its reciprocal:
- Time = \( \frac{31}{5} \times \frac{5}{24} \)
- Time = \( \frac{31 \times 5}{5 \times 24} = \frac{31}{24} \) hours

### Step 4: Convert the time to a mixed number
5. Convert \( \frac{31}{24} \) hours to a mixed number:
- \( 31 \div 24 = 1 \) remainder \( 7 \)
- Therefore, \( \frac{31}{24} = 1 \frac{7}{24} \) hours

### Final Answer
Suman requires \( 1 \frac{7}{24} \) hours to cover `6 (1)/(5)` km.

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