A salmon can go 15 feet downstream on a river in 3 seconds. It takes the salmon 15 seconds to go back up the same 15 feet. Find the speed of the current and the fish in ft/sec

Question

Help! I’m not sure what equation to use for this. Could someone help?

Answer 1

Let x*r be the velocity of the river in ft/sec and x'*s be the velocity of the salmon in ft/sec. Let x and x' be denoted as -1 or 1. If x = -1, then the river is traveling in the negative direction (against the salmon). Conversely, if x =1, the river is traveling a positive direction (with the salmon) For any case, x' = 1 because salmon is always traveling a positive distance whether or not the river impedes it. (*)

We know that if xr + xs = 0, the salmon and the river are in static equilibrium (no motion or distance traveled).

From the given information ("A salmon can go 15 feet downstream in 3 seconds" and "It takes 15 seconds to travel the same distance upstream"), we know that x' = 1 (downstream condition).

For case 1 (downstream), xr +x's = 15 feet/3 sec = 5 ft/s --> r + s = 5

case 2 (upstream), xr +x's = 15 feet/15 sec = 1 ft/sec--> -r + s = 1

To find the velocity of the salmon in relation to the river, the system of equations (1) and (2) must be solved.

Adding equation (1) to (2) yields.... 2s = 6 or s = 3 ft/sec. By (1), it follows that r + 3 = 5

or r = (5-3) = 2 ft/sec

Answer 2

The motion is the sum (or difference) of the speed of the fish and the speed of the water.

Call the Salmon's speed "F", and the water's speed "W". Downstream, the combined speed is F + W, and upstream it is F - W.

The fundamental equation is distance, D = speed * time

We are given the time each way, so we can combine that with our expression for speed to get 2 equations for D:

15 = (F + W) * 3

and

15 = (F - W) * 15

Solve this pair of equations using any of the standard methods

Answer 3

15' distance traveled in 3 sec = 5'/sec speed of the (fish + current).

To go back up, 15'/15 seconds means the net speed is 1'/sec.

f + c = 5 and f - c = 1

Solving these 2 equations yields speed of fish, f = 3 '/sec, and speed of current c = 2 '/sec

Answer 4

Speed (also called rate) is defined as distance divided by time in ft/sec. s = d/t

So the speed of the current is the downstream speed.

15 ft / 3 sec = 5 ft/sec.

The speed of the fish going upstream is

15 ft / 15 sec = 1 ft/sec.

Since the speed of the current is 5 ft/sec and the speed of the fish is 1 ft/sec, this is why it takes the fish more time to go the same distance, it has a slower rate than the current.