The duration it takes for boat 'P' to cover 160 km downstream is equal to the duration it takes to cover 120 km upstream. If the ratio of the speed of boat 'Q' in still water to the speed of the current is the same as that for boat 'P,' with an upstream speed of boat 'Q' being 18 km/hr, determine the time taken by boat 'Q' to travel 144 km downstream.
ATQ, Let the speed of the boat ‘P’ in still water and the speed of the current be ‘p’ km/hr and ‘q’ km/hr, respectively Therefore, downstream speed of boat ‘P’ = (p + q) km/hr Upstream speed of boat ‘P’ = (p – q) km/hr According to the question, {160/(p + q)} = {120/(p – q)} Or, 160p – 160q = 120p + 120q Or, 40p = 280q Or, p:q = 7:1 Therefore, ratio of speed of boat ‘Q’ in still water and the speed of the current = 7:1 Let the speed of the boat ‘Q’ in still water and the speed of the current be 7w km/hr and w km/hr, respectively According to the question, 7w – w = 18 Or, 6w = 18 Or, w = 3 Required time taken = {144/(7w + w)} = 144/24 = 6 hours
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