To find the speed of the stream, we first calculate the downstream and upstream speeds.
Downstream Speed Calculation
The man rows 12 km downstream in 3 hours. The formula for speed is distance divided by time.
Speed downstream = $\frac{Distance}{Time}$ = $\frac{12 \text{ km}}{3 \text{ h}} = 4 \text{ km/h}$
Let $v_m$ be the speed of the man in still water and $v_s$ be the speed of the stream. The downstream speed is the sum of these two speeds:
$v_m + v_s = 4$ km/h (Equation 1)
Upstream Speed Calculation
The man rows 6 km upstream in 2 hours.
Speed upstream = $\frac{Distance}{Time}$ = $\frac{6 \text{ km}}{2 \text{ h}} = 3 \text{ km/h}$
The upstream speed is the difference between the man's speed and the stream's speed:
$v_m - v_s = 3$ km/h (Equation 2)
Stream Speed Determination
To find the speed of the stream ($v_s$), we can subtract Equation 2 from Equation 1:
$(v_m + v_s) - (v_m - v_s) = 4 \text{ km/h} - 3 \text{ km/h}$
$v_m + v_s - v_m + v_s = 1 \text{ km/h}$
$2v_s = 1 \text{ km/h}$
$v_s = \frac{1}{2} \text{ km/h}$
$v_s = 0.5 \text{ km/h}$
The speed of the stream is 0.5 km/h.
Important Questions from Boat and River
A boat goes 30 km upstream in 3 hours and downstream in 1 hour. How much time (in hours) will this boat take to cover 60 km in still water?
The speed of a motorboat in still water is 20 km/h. It travels 150 km downstream and then returns to the starting point. If the round trip takes a total of 16 hours, what is the speed (in km/h) of the flow of river?
The time taken by a boat to travel 13 km downstream is the same as time taken by it to travel 7 km upstream. If the speed of the stream is 3 km/h, then how much time (in hours) will it take to travel a distance of 44.8 km in still water?
A man can row a distance of 8 km downstream in a certain time and can row 6 km upstream in the same time. If he rows 24 km upstream and the same distance downstream in \(1\frac{3}{4}\) hours, then the speed (in km/h) of the current is:
A boat goes 27 km upstream and 33 km downstream in 6 hours. In the same time it can go 36 km upstream and 22 km downstream. How much time will it take to go 36 km upstream and 44 km downstream?
