Explanation:
Let's solve this problem step by step.
Let's assume the speed at which salmon normally swim, with no current, is 'n' miles per hour.
When the salmon swims downstream (with the current), it is helped by the current's speed, so its effective speed is the sum of its normal swimming speed and the current's speed. Therefore, when swimming downstream, the salmon's speed is (n + 5) miles per hour.
When the salmon swims upstream (against the current), it faces resistance from the current, so its effective speed is the difference between its normal swimming speed and the current's speed. Therefore, when swimming upstream, the salmon's speed is (n - 5) miles per hour.
We are given that the salmon can swim 25 miles downstream in the same amount of time it takes to swim 15 miles upstream. Let's set up an equation to represent this information:
Time taken to swim downstream = Time taken to swim upstream
Distance / Speed downstream = Distance / Speed upstream
25 / (n + 5) = 15 / (n - 5)
To solve this equation, we can cross-multiply:
25(n - 5) = 15(n + 5)
25n - 125 = 15n + 75
25n - 15n = 75 + 125
10n = 200
n = 20
Therefore, the salmon normally swims at a speed of 20 miles per hour with no current.