A motor boat goes downstream from point A to B ,which is 36 km away from point A, and then returns to A. If actual speed of the boat in still water is 7km/hour ,and the total upstream and downstream journey takes 21 hours .What must be the actual speed of boat for the journey from A to B to take exactly 108 minutes ?

Speed of boat in still water is 7km/hour Let the Speed of Stream be x Km/hour 36/(7+x) + 36/(7-x) = 21 24 = 49- x^{2} x = 5 km/hour Now, the speed of Boat for the journey from A to B to take time 108 minutes is Speed of boat = y km/hour , Speed of stream = 5km/hour , Time = 108 minutes (y+5) = (36×60)/108 = 20km/hour y+5 = 20 y = 15km/hour ∴ Speed of Boat must be 15km/hour

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