Question
The speed of the boat A and B in still water are in the
ratio 15:13. The speed of the current for both boats is 16 km/hr. If the sum of time taken by boat A in downstream to travel 184 km and time taken by boat B to travel 40 km in upstream is 8 hours. Find the sum of the speed of boat A in upstream and B in downstream.Solution
Let the speed of the boats ‘A and ‘B’ in still water be ‘15x’ km/hr and ‘13x’ km/hr, repectively Speed of boat ‘A’ in downstream = (15x+16) km/hr Speed of boat ‘B’ in upstream = (13x-16) km/hr According to the question, {184/((15x+16) )}+{40/((13x-16) )} = 8 [23/(15x+16)] + [5/(13x-16)] = 1 23(13x-16) + 5(15x+16) = (15x+16)(13x-16) 299x - 368 + 75x + 80 = 195x2 - 240x + 208x - 256 374x - 288 = 195x2 - 32x - 256 195x2 - 406x - 32 = 0 on solving we get value, x=2 Speed of the boat A and B in still water is 30km/hr and 26 km/hr . Speed of boat A in upstream = 30-16 = 14 km/hr Speed of the boat B in downstream = 26+16 = 42 km/hr Required sum = 14km/hr +42 km/hr = 56 km/hr.
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