Question
The ratio of Alex's boat speed in calm water to the
speed of the stream is 5:1, respectively. If the boat can traverse 144 km against the current and 360 km with the current in a total time of 8 hours, determine how long it takes for the boat to cover a distance of 192 km in calm water.Solution
ATQ, Let speed of boat in still water and speed of stream is ‘5a’ km/h and ‘a’ km/h, respectively. Speed of boat in upstream = 5a – a = 4a km/h Speed of boat in downstream = 5a + a = 6a km/h So, [(144/4a) + (360/6a)] = 8 Or, [(36/a) + (60/6a)] = 8 Or, a = (96/8) = 12 So, speed of boat in still water = 12 × 5 = 60 km/h Desired time = 192/60 = 3.2 hours = 3 hours 12 minutes
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