A boat sails 180 km downstream and half of that distance

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