Question
A boat sails 180 km downstream and half of that distance
upstream in 12 hours. If the stream’s speed is 50% less than that of the boat in still water, determine the time required to travel 75 km upstream and 225 km downstream.Solution
ATQ,
Let, the speed of the boat in still water = 4x kmph
Speed of the stream = 4x × (1 – 0.5) = 2x kmph
Downstream speed of the boat = (4x + 2x) = 6x kmph
Upstream speed of the boat = (4x – 2x) = 2x kmph
Distance travelled in upstream = (1/2) × 180 = 90 km
Now,
(180 / 6x) + (90 / 2x) = 12
Or, (30/x) + (45/x) = 12
Or, (75/x) = 12
So, x = 75 / 12 = 6.25
Now,
Upstream speed = 2x = 12.5 kmph
Downstream speed = 6x = 37.5 kmph
Time to travel 75 km upstream = 75 / 12.5 = 6 hours
Time to travel 225 km downstream = 225 / 37.5 = 6 hours
Total time = 12 hours
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