a sailor goes 8km down stream in 40 minutes and return in 1 hour. find the speed of water and sailor in still water.

Answer: Speed of sailor in still water = 10 km/h, Speed of water (stream) = 2 km/h

Step-by-step solution

Step 1: Define variables and convert units

Let $u$ denote the sailor's speed in still water and $v$ denote the speed of the stream, both in km/h. The downstream distance is $8\text{ km}$ covered in $40\text{ minutes}$ , which equals $\frac{2}{3}\text{ hour}$ . The upstream return journey covers the same distance of $8\text{ km}$ in $1\text{ hour}$ .

Step 2: Calculate downstream and upstream speeds

Downstream speed is distance divided by time, giving $\frac{8}{\frac{2}{3}} = 12\text{ km/h}$ . Since the stream aids the boat, downstream speed is $u + v = 12$ . Upstream speed is $\frac{8}{1} = 8\text{ km/h}$ , where the stream opposes the boat, so $u - v = 8$ .

Step 3: Solve the system of equations

Adding equation (1) and equation (2) eliminates $v$ , yielding $2u = 20$ , so $u = 10\text{ km/h}$ . Subtracting equation (2) from equation (1) eliminates $u$ , giving $2v = 4$ , so $v = 2\text{ km/h}$ .

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