SOLUTION: a salmon swims 100 m in 8min downstream upstream it would take the fish 20 min. what is the rate of the current and the speed of the fish.

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Question 947422: a salmon swims 100 m in 8min downstream upstream it would take the fish 20 min. what is the rate of the current and the speed of the fish.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the fish in meters/min
Let +c+ = the speed oif the current in meters/min
----------------------
Equation for downstream:
(1) +100+=+%28+s+%2B+c+%29%2A8+
Equation for upstream:
(2) +100+=+%28+s++-+c+%29%2A20+
--------------------------
(1) +s+%2B+c+=+25%2F2+
and
(2) +s+-+c+=+5+
--------------------
Add the equations
+2s+=+10%2F2+%2B+25%2F2+
+2s+=+35%2F2+
+s+=+35%2F4+
+s+=+8.75+
and
(1) +35%2F4+%2B+c+=+25%2F2+
(1) +c+=+50%2F4+-+35%2F4+
(1) +c+=+15%2F4+
(1) +c+=+3.75+
The speed of the fish is 8.75 meters/min
The speed oif the current is 3.75 meters/min
----------------
check:
(2) +s+-+c+=+5+
(2) +8.75+-+3.75+=+5+
(2) +5+=+5+
and
(1) +100+=+%28+s+%2B+c+%29%2A8+
(1) +100+=+%28+8.75+%2B+3.75+%29%2A8+
(1) +100+=+12.5%2A8+
(1) +100+=+100+
OK