Average speed trick for equal distances: 2xy ÷ (x + y)
समान दूरी पर औसत चाल की ट्रिक: 2xy ÷ (x + y)
When you go somewhere at one speed and come back the same distance at another, the average speed is 2xy ÷ (x + y) — not the simple average of the two speeds.
जब जाना एक चाल से और उतनी ही दूरी लौटना दूसरी चाल से हो, तो औसत चाल 2xy ÷ (x + y) होती है — दोनों चालों का साधारण औसत नहीं।
The formula
Average speed = total distance ÷ total time. For two equal distances at speeds x and y this always simplifies to 2xy ÷ (x + y).
- Multiply the two speeds and double it: 2xy.
- Divide by the sum of the speeds: x + y.
Why the simple average is wrong
You spend more time at the slower speed, so the slower speed pulls the average down. The answer is always below (x + y) ÷ 2. If an option equals the simple average, it is a trap.
Equal time is different
If the two speeds are kept for equal TIME (not equal distance), the average speed is simply (x + y) ÷ 2. Read the question carefully.
Try it yourself · अभ्यास
- Up a hill at 45 km/h, down the same road at 55 km/h. Average speed?
Show answer
2 × 45 × 55 ÷ 100 = 49.5 km/h
- Speeds 60 and 40 km/h for equal time. Average speed?
Show answer
(60 + 40) ÷ 2 = 50 km/h