A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is
(A) 600 km/hr.
(B) 583.33 km/hr.
(C) $100\sqrt{35}$ km/hr.
(D) 620 km/hr.

Question

Accepted Answer

> [!TLDR]
> Average speed for equal distances = harmonic mean of the two speeds = $\dfrac{2	imes500	imes700}{500+700}=583.33$ km/hr.

### Step 1 — Choose the right average
The helicopter covers the **same distance** A→B and B→A at different speeds. When the distances are equal, average speed is the **harmonic mean** of the speeds:
$$\bar V = \dfrac{2 v_1 v_2}{v_1 + v_2}.$$

### Step 2 — Substitute
$$\bar V = \dfrac{2 	imes 500 	imes 700}{500 + 700} = \dfrac{7{,}00{,}000}{1{,}200} = 583.33	ext{ km/hr}.$$

### Step 3 — Why not 600?
The **arithmetic** mean $	frac{500+700}{2}=600$ (option A) is wrong here: the helicopter spends **more time** at the slower speed, pulling the true average below 600. …

Harmonic Mean

The governing formula

Why it works

Worked illustration …

Step 1 — Choose the right average

Step 2 — Substitute

Step 3 — Why not 600?

Step 1 — Choose the right average

Step 2 — Substitute

Step 3 — Why not 600?

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