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.

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