Sourav completes a journey in **5½ hours**. If he covers half of the distance at **5 km/h** and the remaining half at **6 km/h**, then find the total distance covered by him.

Question

Accepted Answer

#### Step 1: Represent the Problem Mathematically
Let the total distance be $$ D $$.  
- Half the distance = $$ \frac{D}{2} $$.  
- Speed for the first half = $$ 5 \, 	ext{km/h} $$.  
- Speed for the second half = $$ 6 \, 	ext{km/h} $$.

The time taken for each half is:  
1. Time for first half:  
   $$ 	ext{Time}_1 = \frac{\frac{D}{2}}{5} = \frac{D}{10}. $$

2. Time for second half:  
   $$ 	ext{Time}_2 = \frac{\frac{D}{2}}{6} = \frac{D}{12}. $$

The total time is given as **5½ hours** or $$ 5.5 \, 	ext{hours} $$:  
$$
	ext{Total Time} = 	ext{Time}_1 + 	ext{Time}_2.
$$

#### Step 2: Set Up the Equation
Substitute the values:  
$$
5.5 = \frac{D}{10} + \frac{D}{12}.
$$

Simplify the equation by finding a common denominator (LCM of 10 and 12 is 60):  
$$
5.5 = \frac{6D}{60} + \frac{5D}{60}.
$$  
$$
5.5 = \frac{11D}{60}.
$$

Multiply through by 60 to solve for $$ D $$:  
$$
11D = 60 	imes 5.5.
$$  
$$
11D = 330.
$$  
$$
D = \frac{330}{11} = 30.
$$

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#### Step 3: Verify Results
The total distance covered by Sourav is **30 km**.

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Thus, the correct answer is **(a) 30 km**.

Answer

Answer

Answer