A salmon can swim 20 feet/sec downstream in a river. The salmon swims upstream at a rate of 6 feet/sec. Find the speed of the current.
How do I set up the equation?
u+c = 20
u-c = 6
------------subtract
To set up the equation, we can use the concept of relative velocity. Let's assume the speed of the current as "c" and the speed of the salmon in still water (without the current) as "s".
When the salmon swims downstream, its effective speed is the sum of its swimming speed and the current speed: s + c = 20 feet/sec.
When the salmon swims upstream, its effective speed is the difference between its swimming speed and the current speed: s - c = 6 feet/sec.
Now we have a system of equations. We can solve these equations simultaneously to find the value of "c," which represents the speed of the current.
To set up the equation, let's assume the speed of the current is represented by 'c' (in feet/second).
When the salmon is swimming downstream, its effective speed will be the sum of its own swimming speed (20 feet/sec) and the current speed (c feet/sec). Therefore, the equation for the downstream speed can be written as:
Downstream speed = Salmon's swimming speed + Current speed
20 feet/sec = 20 feet/sec + c feet/sec
When the salmon is swimming upstream, its effective speed will be the difference between its own swimming speed (6 feet/sec) and the current speed (c feet/sec). Therefore, the equation for the upstream speed can be written as:
Upstream speed = Salmon's swimming speed - Current speed
6 feet/sec = 6 feet/sec - c feet/sec
Now, you can solve this system of equations to find the value of 'c', which represents the speed of the current.