Question
The speed ratio of a stream to the upstream speed of a
boat is 1:9. A boat takes 2 hours and 30 minutes to travel 82.5 km downstream. Determine the time (in minutes) the boat will take to travel 54 km in still water.Solution
Let the speed of boat in still water and speed of stream be 'v' and 'x' km/h respectively. ATQ, x:(v - x) = 1:9 Or, 9x = v - x Or, 'v' = 10x -------- (I) Downstream speed = v + x = 10x + x = '11x' km/h So, 11x = (82.5/2.5) Or, 11x = 33 So, 'x' = 3 On putting value of 'x' in equation (I) , We get, 'v' = 10 X 3 = 30 Therefore, required time = (54/30) = 1.8 hours = 1.8 X 60 = 108 minutes
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