Question
A boat covers 144 km upstream and 192 km downstream in
equal durations. If it takes 5 hours to travel 140 km in still water, determine the time the boat would take to travel a total of 128 km — going upstream and returning downstream.Solution
ATQ,
Let speed of boat in upstream and downstream is ‘x’ km/h and ‘y’ km/h respectively.
So, 144/x = 192/y
Or, y/x = 192/144 = 4/3
Or, y = 4x/3
So, speed of boat in still water = (x + y)/2 = (4x/3 + x)/2 = 7x/6 km/h
So, 7x/6 = 140/5
Or, x = 24 km/h
Speed of boat in upstream = 24 km/h
Speed of boat in downstream = 4 × 24/3 = 32 km/h
Desired time = 128/24 + 128/32 = 5 hours 20 minutes + 4 hours = 9 hours 20 minutes.
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