Question
The speed of the boat exceeds the
speed of the stream by 66.67%. Determine the speed of the boat in still water. Statement I: The time required for the boat to travel (12d−6)km downstream is the same as the time required to travel (d+18) km upstream. Statement II: The boat can travel 91.2km downstream in 11.4hours.Solution
ATQ, Let speed of boat in still water be 'v' & speed of stream be 's' Then, v:s = 5:3 v+s = 8 [downstream speed] & v – s = 2 [upstream speed] From St.I we have Given time is constant, so ratio of speed = ratio of distance covered. D1/D2 = S1/S2 (12-d)/(d+18) = 8/2 So here by determining 'd' we can determine and determine the value of 'd' but still we do not have the time. So we still cannot determine the speed of boat in still water. Thus statement I is not sufficient to answer the question. From St.I we have Downstream speed (v+s) = 91.2/11.4 = 8 km/h v +s= 8u = 8 km/h So, v = 5u = 5km/h Thus statement II is sufficient to answer the question
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