Two drones, Alpha and Beta, take off simultaneously from two ground stations separated by a straight distance of $120\text{ km}$ and fly directly towards each other. Drone Alpha flies at a constant ground speed of $50\text{ km/h}$, and Drone Beta flies at $70\text{ km/h}$. After how many minutes from takeoff will the two drones cross each other in the air?

Answer Key:

60

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Relative Speed Concept:** When two objects travel directly towards each other, their relative speed of approach is the sum of their individual speeds. 2. **Stage 2: Relative Velocity Calculation:** * $V_{rel} = V_{Alpha} + V_{Beta} = 50\text{ km/h} + 70\text{ km/h} = 120\text{ km/h}$. 3. **Stage 3: Time Calculation:** * Total distance $D = 120\text{ km}$. * Time $t = \frac{D}{V_{rel}} = \frac{120\text{ km}}{120\text{ km/h}} = 1.0\text{ hour}$. 4. **Stage 4: Unit Conversion:** * The question asks for minutes: $1.0\text{ hour} = 60\text{ minutes}$. 5. **Stage 5: Common Trap:** Entering 1 (hours) instead of 60 (minutes).

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