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Speed of the boat in still water = 5 km /hr
Width of the river = 1 km
Time taken by the boat to cross the river = 15 minutes = 15/60 hr = 1/4 hr
Let the velocity of the river be x km/hr.
Distance covered by the boat in 1/4 hr = 5/4 km = 1.25 km
Because of the flow of the river the boat will move in the direction of AC, which is the shortest possible path for the boat.
∴ AC = 1.25 km
AB (Width of the river) = 1 km
BC is the other bank of the river so the width AB of the river will be perpendicular to BC .i.e., ∠B = 90°
In ΔABC by Pythagoras theorem,
(AB)2 + (BC)2 = (AC)2
⇒ (1)2 + (BC)2 = (1. 25)2
⇒ (BC)2 = (1.25)2 – (1)2
⇒ (BC)2 = 1.5625 – 1
⇒ (BC)2 = 0.5625
⇒ BC = 0.75 km
Which means that distance covered by the river water in 15 minutes is 0.25 km.
∴ Velocity of the river = 0.75/(15/60) km/hr
= 3 km/hr
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