Question
Ratio of still water speeds of three boats is 3:4:5. The
first boat travels downstream, the second and third boats travel upstream. They travel in streams of speed ratio 2:2:3 so that the ratio of effective speed of the boats is 5:2:2. If the effective speed of the first boat is 15 km/hr more than the effective speed of the third boat, what is the sum of their still water speeds?Solution
Ratio of their still water speeds = 3:4:5 Let their still water speeds be 3x, 4x and 5x Stream speed is in the ratio 2:2:3 Let the stream speeds be 2y, 2y and 3y ∴ Their effective speeds are (3x + 2y), (4x - 2y), (5x - 3y) respectively. (3x + 2y): (4x - 2y): (5x - 3y) = 5:2:2 => (3x + 2y)/5 = (4x - 2y)/2 => 20x - 10y = 6x + 4y => 14x = 14y => x = y ∴ Their effective speeds are 5x, 2x and 2x respectively. Given, 5x = 2x + 15 => 3x = 15 => x = 5 Sum of their still water speeds = 3x + 4x + 5x = 12x = 12 ×  5 = 60 km/hr.
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