A swimmer crosses a flowing stream of width `d` to and fro normal to the flow of the river at time `t_(1)`. The time taken to cover the same distance up and down the stream is `t_(2)`. If `t_(3)` is the time the swimmer would take to swim a distance `2d` in still water, then relation between `t_(1),t_(2)`&`t_(3)`.

Explanation

To solve the problem, we will analyze the motion of the swimmer in three different scenarios: crossing the river, swimming upstream, and swimming downstream. We will derive the relationships between the times taken in each case.

### Step 1: Analyze the first case (Crossing the river)

The swimmer crosses the river of width \( d \) perpendicular to the flow of the river. Let:
- \( u \) = speed of the swimmer in still water
- \( v \) = speed of the river

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