Question

Amit cycled from his house to the garden at speed of 12 km/hr and came back to his house at the speed of 6 km/hr. if the total time taken by Amit to complete the journey was 6 hours, then find the distance between Amit’s House and garden?

• A. \(32 \text{ km} \)
• B. \(28 \text{ km} \)
• C. \(24 \text{ km} \)
• D. \(36 \text{ km} \)

Hint:

To avoid calculation errors, notice that the speed back (6) is half the speed there (12). This means the time taken to return will be double the time taken to go! (2 hrs going, 4 hrs returning).

Answer 1

The Correct Option is C

Concept: When a person travels the same distance at two different speeds \(v_1\) and \(v_2\), and the total time taken for the entire journey is \(T\), the distance \(d\) can be found using the formula: \[ d = \frac{v_1 \times v_2}{v_1 + v_2} \times T \] Alternatively, Average Speed = \( \frac{2v_1v_2}{v_1 + v_2} \), and Total Distance (\(2d\)) = Average Speed \( \times \) Total Time.
Step 1: Identify the speeds and total time.
Speed to garden (\(v_1\)) = 12 km/hr.
Speed back home (\(v_2\)) = 6 km/hr.
Total time (\(T\)) = 6 hours.

Step 2: Apply the distance formula.
\[ d = \frac{12 \times 6}{12 + 6} \times 6 \] \[ d = \frac{72}{18} \times 6 = 4 \times 6 = 24 \text{ km}. \]