Calculate Rowing Stream Speed
This solution explains how to calculate the speed of the stream using upstream and downstream travel information.
Determine Speeds from Distance and Time
Let $r$ be the rower's speed in still water and $s$ be the speed of the stream.
Upstream Journey:
- Distance = 144 km
- Time = 12 hours
- Upstream Speed = $r - s$
Using Speed = Distance / Time, the upstream speed is:
$r - s = \frac{144 \text{ km}}{12 \text{ hours}} = 12$ km/h
Downstream Journey:
- Distance = 144 km
- Time = 9 hours
- Downstream Speed = $r + s$
The downstream speed is:
$r + s = \frac{144 \text{ km}}{9 \text{ hours}} = 16$ km/h
Solve for Stream Speed
We have a system of two linear equations:
- $r - s = 12$
- $r + s = 16$
To find the speed of the stream ($s$), subtract the first equation from the second:
$(r + s) - (r - s) = 16 - 12$
$2s = 4$
$s = \frac{4}{2}$
$s = 2$ km/h
Conclusion
The speed of the stream is 2 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?
