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The question from the image asks:

**Dayal can walk at a speed of \(3 \frac{9}{10}\) km/h. Tanmay can walk \(1 \frac{3}{13}\) times as fast as Dayal. Find the difference between their speeds. Show your work.**

### Step 1: Convert mixed fractions to improper fractions
1. **Dayal's speed:**
   \(3 \frac{9}{10}\) km/h can be written as:
   \[
   3 \frac{9}{10} = \frac{3 \times 10 + 9}{10} = \frac{39}{10} \text{ km/h}.
   \]

2. **Tanmay's speed factor:**
   \(1 \frac{3}{13}\) can be written as:
   \[
   1 \frac{3}{13} = \frac{1 \times 13 + 3}{13} = \frac{16}{13}.
   \]

### Step 2: Find Tanmay's speed
Tanmay walks \(1 \frac{3}{13}\) times faster than Dayal. So, we multiply Dayal's speed by this factor:
\[
\text{Tanmay's speed} = \frac{39}{10} \times \frac{16}{13}.
\]
Multiplying the fractions:
\[
\frac{39}{10} \times \frac{16}{13} = \frac{39 \times 16}{10 \times 13} = \frac{624}{130}.
\]

Simplify \( \frac{624}{130} \):
\[
\frac{624}{130} = \frac{312}{65} \text{ km/h}.
\]

### Step 3: Find the difference between their speeds
Now, subtract Dayal's speed from Tanmay's speed:
\[
\text{Difference} = \frac{312}{65} - \frac{39}{10}.
\]

To subtract, first find a common denominator. The least common denominator between 65 and 10 is 130:
\[
\frac{312}{65} = \frac{624}{130}, \quad \frac{39}{10} = \frac{507}{130}.
\]

Now subtract:
\[
\text{Difference} = \frac{624}{130} - \frac{507}{130} = \frac{117}{130}.
\]

So, the difference in their speeds is:
\[
\frac{117}{130} \text{ km/h}.
\]

This is approximately \(0.9\) km/h.

Would you like a detailed explanation for any step or have additional questions?

### Related Questions:
1. How do you convert mixed fractions into improper fractions?
2. What is the process for multiplying two fractions?
3. How can you simplify a fraction after multiplication?
4. What are the steps for finding the least common denominator?
5. How do you perform fraction subtraction with different denominators?

### Tip:
When working with mixed fractions, always convert them to improper fractions before performing any arithmetic operations like multiplication or division.

Dayal can walk at a speed of 3 9/10 km/h. Tanmay can walk 1 3/13 times as fast as Dayal. Find the difference between their speeds. Show your work.

This problem compares the walking speeds of Dayal and Tanmay using mixed fractions and fraction multiplication. Learn how to convert mixed fractions to improper fractions, multiply them, and find the speed difference using fraction subtraction. Suitable for students in Grades 6-8.

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