Before rain a boat can cover 90 km in still water and the same distance upstream in 6 hours and 9 hours, respectively. Due to the rain the speed of the stream increased by 20% and the speed of the boat decreased by (1/3) of its initial speed. Find the difference of time taken by the boat to travel 176 km downstream and 76 km upstream .

Solution

Let the speed of the boat in still water by x km/hr and speed of the stream be y km/hr. As per the question Time taken by the boat to cover 90 km in still water = (90/x) = 6 x= 15km/hr Time taken by the boat to travel 90 km in upstream = (90/15-y) = 9   = 90 = 135-9y   = 9y = 45    = y = 5 km/hr. Change in speed of boat and stream Boat = 15*(2/3) = 10 km/hr Stream = 5*(6/5) = 6 km/hr. Speed downstream = 10+6 = 16 km/hr. Time taken by boat to cover 176 km = 176/16 = 11 hr. Upstream speed = 10-6 = 4 km/hr. Time taken by boat to cover 76 km = 76/4 = 19 hrs Required difference = 19hr – 11 hr. = 8 hrs.