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A salmon is swimming in a river that is flowing downstream at a speed of 2 miles per hour. The slamon can swim 12 miles upstream in the same amount of time it would take 24 miles downstream. What is the speed of the salmon in still water?

User Hari Das
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Answer:

The speed of the salmon in still water is 6 mi/h

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

User Ayo I
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