Correct option is D
Given:
- Rajesh travels half the distance at 50 km/h
- He wants his overall average speed to be 100 km/h
We are to find out how fast he must travel the remaining half to make this possible — or determine if it's even possible.
Concept Used:
Average speed is not the average of two speeds.
It is calculated by:
Average speed = Total Distance ÷ Total Time
Solution:
Assume total distance = 2 km (for simplicity)
Step 1: First half of distance = 1 km at 50 km/h
- Time taken = Distance ÷ Speed = 1 ÷ 50 = 1/50 hours
Step 2: Let the speed needed for second half be x km/h
- Time taken = 1 ÷ x
Step 3: Total time = 1/50 + 1/x
Average speed = 2 ÷ (1/50 + 1/x)
Set this equal to 100:
2 ÷ (1/50 + 1/x) = 100
Cross-multiplying:
1/50 + 1/x = 2/100 = 1/50
Now observe:
1/50 + 1/x = 1/50 → subtract 1/50 from both sides
1/x = 0 → Not possible
This implies x must be infinite, i.e., Rajesh would have to drive at infinite speed to achieve an average of 100 km/h.
Final Answer: (D) Average speed of 100 km/h is not possible in this case.
