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 difference between 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, (2444x – 3008) + (600x+640) = 8*(195x² –32x-256) 3004x-2368 = 1560x² –256x-2048 1560x² – 3260x + 320 = 0 78x² – 163x + 16 = 0 X= 1.98 or 0.10 X= 2 approx. 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.