Question

Sourav completes a journey in \(5\frac12\) hours. If he covers half of the distance at \( 5\ km/h\) and the remaining distance at \(6\  km/h\), then find the total distance covered by him.

• A. 30 km
• B. 35 km
• C. 33 km
• D. 39 km

Answer 1

The Correct Option is A

Sourav completes a journey in \(5\frac{1}{2}\) hours. If he covers half of the distance at 5\ \text{km/h} and the remaining distance at 6\ \text{km/h}, we need to find the total distance. Let the total distance be \(d\) km.

The journey can be broken into two parts: the first half of the journey (\(\frac{d}{2}\)) is traveled at 5\ \text{km/h}, and the second half (\(\frac{d}{2}\)) at 6\ \text{km/h}.

Step 1: Calculate the time to travel the first half:

\[\text{Time}_{\text{first half}} = \frac{\frac{d}{2}}{5} = \frac{d}{10}\]

Step 2: Calculate the time to travel the second half:

\[\text{Time}_{\text{second half}} = \frac{\frac{d}{2}}{6} = \frac{d}{12}\]

Step 3: Calculate the total time and set it equal to the journey time, \(5\frac{1}{2}\) hours:

\[\frac{d}{10} + \frac{d}{12} = 5.5\]

To solve this, find a common denominator (60):

\[\frac{6d}{60} + \frac{5d}{60} = 5.5 \Rightarrow \frac{11d}{60} = 5.5\]

Step 4: Solve for \(d\):

\[11d = 5.5 \times 60\]

\[11d = 330\]

\[d = \frac{330}{11} = 30\]

Therefore, the total distance covered by Sourav is 30 km.