Answer:
The speed of the salmon in still water is 6 mi/h
Step-by-step explanation:
When an object moves with a speed So (So measured in still water) in a river with speed Sr:
If the object moves along the current (downstream), then the actual speed of the object will be:
S = So + Sr
If the object moves upstream, then the velocity will be:
S = So - Sr
In this case we know the speed of the river downstream is 2 mi/h
Sr = 2mi/h
And we know that the salmon can swim 12 miles upstream in the same time (T) that it can swim 24 miles downstream.
Here you need to remember the relation:
Distance = Time*Speed.
Then we know that:
24 mi = (So + 2mi/h)*T
12 mi = (So - 2mi/h)*T
Now we can take the quotient of these two equations to get:
(24mi/12mi) = ( (So + 2mi/h)*T)/((So - 2mi/h)*T)
2 = (So + 2mi/h)/(So - 2mi/h)
Let's multiply both sides by the denominator of the right part:
2*(So - 2mi/h) = (So + 2mi/h)
2*So - 4mi/h = So + 2mi/h
Now we need to isolate So, the speed of the salmon in still water:
2*So - So = 2mi/h + 4mi/h
So = 6mi/h
The speed of the salmon in still water is 6 mi/h
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