Question

A person covers the first half of the distance with 6 m/s and the rest half with 9 m/s and 15 m/s in two equal time intervals. Find the average speed of the journey.

• A. 12 m/s
• B. 9 m/s
• C. 10 m/s
• D. 8 m/s

Answer 1

The Correct Option is D

To find the average speed of the journey, let's break down the journey into clear parts:

1. The journey consists of two halves:
   • The first half of the distance is covered at a speed of 6 m/s.
   • The second half of the distance is covered in two intervals of equal time with speeds of 9 m/s and 15 m/s, respectively.
2. Let the total distance be 2D. Hence, each half is D.
3. For the first half:
   • Distance = D, Speed = 6 m/s.
   • Time taken = \frac{D}{6}.
4. For the second half, covered in two equal time intervals with speeds of 9 m/s and 15 m/s:
   • Let the time taken for each interval be t.
   • In the first interval, distance = 9t.
   • In the second interval, distance = 15t.
   • Thus, 9t + 15t = D \implies 24t = D.
   • Therefore, t = \frac{D}{24}.
5. Total time for the second half = t + t = \frac{D}{12}.
6. Total time for the journey:
   • = Time for the first half + Time for the second half.
   • = \frac{D}{6} + \frac{D}{12}
   • = \frac{2D + D}{12} = \frac{3D}{12} = \frac{D}{4}.
7. Average speed of the entire journey:
   • = Total distance / Total time.
   • = \frac{2D}{\frac{D}{4}}
   • = 8 \text{ m/s}.

Thus, the average speed of the journey is 8 m/s. This matches the given correct answer.