The duration it takes for boat 'P' to cover 160 km

Solution

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