Answer:
To solve the problem, we can use the formula:
Total swim time = (time swimming downstream) + (time swimming upstream)
Let's call the speed of the river's current "c". When swimming downstream, the participant's effective speed is 2 + c miles per hour. When swimming upstream, the effective speed is 2 - c miles per hour.
Using the formula above and plugging in the given values, we get:
1.25 = (1.2 / (2 + c)) + (1.2 / (2 - c))
Simplifying this equation requires some algebraic manipulation, but we can eventually arrive at:
c^2 - 1.44 = 0
Solving for c gives us:
c = ±1.2
Since the participant is swimming both downstream and upstream, we know that the current must be flowing in one direction only. Therefore, we take only the positive solution:
The river's current is 1.2 miles per hour.