A salmon can go 100 feet downstream on a river in 2 seconds. It takes 20 seconds for this salmon to go back upstream the same 100 feet. Find the speed of the current. pls help me

Answer 1

Let "x" be the velocity that the salmon swims and let "y" be the velocity of the river water. Going downstream the overall velocity will be x + y and going upstream the overall velocity will be x - y.

Going downstream, the total velocity is (100 ft)/(2 seconds) = 50 ft/s so x + y = 50

Going upstream, the total velocity is (100 feet)/(20 seconds) = 5 ft/s so x - y = 5 or x = y + 5

If x = y + 5, then we can re-write the first equation (x + y = 50) as (y + 5) + y = 50

(y + 5) + y = 50

2y + 5 = 50

2y = 45

y = 22.5 so the velocity of the current (river water) is 22.5 ft/s

As a side note, the velocity of the salmon can be calculated from x = y + 5 or x = 22.5 + 5 = 27.5 ft/s

Answer 2

100/2 = 50 (feet/sec) ← speed upstream

100/20 = 5 (feet/sec) ← speed downstream

Let “x” be the speed of the salmon

Let “y” be the speed of the current

Writing equations:

x + y = 50

x - y = 5

2x = 55, x = 27.5

y = 27.5 - 5 = 22.5 ← speed of the current

Answer 3

Hi...

Consider that the current helps the salmon when its going downstream and works against the salmon when its going upstream. This is a problem that requires the solution of a system of linear equations.

Take x = rate of the salmon (in calm waters)

Take y = rate of the current

Remember that distance, d = speed/rate (r) x time (t)

So the rate downstream will be equal to (x + y) because the current helps the salmon travel further faster

So the rate upstream will be equal to (x - y) because the current works against the salmon

Eq 1; 100 = (x + y) 2 ... d = r • t

Eq 2; 100 = (x - y) 20 ... d = r • t

100 = 2x + 2y

100 = 20x - 20y

You can chose one variable to cancel out by manipulating one of the equations so that when you add the two equations, you are left with the other variable. In this case, divide Eq 2 by -10

100 = 2x + 2y

-10 = -2x + 2y

Adding the equations together, the 2x and -2x terms cancel out

90 = 4y

y = 22,5 ft/sec - this is the rate of the current

Plug this value of y into either of the two equations to find x

100 = 2x + 2(22.5)

100 = 2x + 45

55 = 2x

x = 27.5 ft/sec

And that would make sense because with the current helping the salmon, the rate is (x + y) = 50ft/sec which is how it is able to travel 100ft in 2 sec. And swimming upstream the net rate is (x - y) = 5ft/sec so it takes 10 times longer to cover the same distance.

Hope this helps :)