Rohan finishes a journey by scooter in 5 hours. He travels the first half of the journey at \( 30 \mathrm{~km} / \mathrm{h} \) and the second half of the journey at \( 20 \mathrm{~km} / \mathrm{hr} \) . The distance covered by him is:
Step-by-step Solution:
Here are two common methods to solve this problem.
1. Calculate the Average Speed: - Since the journey is split into two equal distances at different speeds (S1 and S2), we must use the harmonic mean for the average speed: Avg Speed = (2 × S1 × S2) / (S1 + S2).
- Avg Speed = (2 × 30 × 20) / (30 + 20)
- Avg Speed = 1200 / 50 = 24 km/hr.
2. Calculate Total Distance: - Total Distance = Average Speed × Total Time
- Total Distance = 24 km/hr × 5 hours = 120 km.
1. Set Up the Equation: - Let the total distance be D km. The journey is split into two halves of D/2 km.
- We know that Time = Distance / Speed, and the total time is 5 hours.
- (Time for 1st half) + (Time for 2nd half) = 5 hours
- (D/2 ÷ 30) + (D/2 ÷ 20) = 5
- This simplifies to: D/60 + D/40 = 5
2. Solve for D: - Using a common denominator of 120:
- (2D/120) + (3D/120) = 5
- 5D / 120 = 5
- This means D = 120 km.
Final Answer: The total distance covered is 120 km.