Question
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.
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