In one hour, a boat goes 12 km along the stream and 6 km against the stream.
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In one hour, a boat goes 12 km along the stream and 6 km against the stream. The speed of the boat in still water (in km/hr) is:
Show answer & explanation
The speed of a boat in still water is the arithmetic mean of its downstream speed and its upstream speed.
Step-by-step Derivation:
Step 1: Identify the downstream speed (speed along the stream). Since the boat covers 12 km in 1 hour, Downstream Speed (u) = 12 km/hr.
Step 2: Identify the upstream speed (speed against the stream). Since the boat covers 6 km in 1 hour, Upstream Speed (v) = 6 km/hr.
Step 3: Use the formula for the speed of a boat in still water: Speed in still water = (Downstream Speed + Upstream Speed) / 2.
Step 4: Substitute the values: Speed = (12 + 6) / 2 = 18 / 2 = 9 km/hr.