A man rows across a flowing river in time `t_(1)` and rows an equal distance downstream in time `t_(2)`. Calculate the ratio `t_(1):t_(2)` if the speed of man in still water is `5 m//s` and speed of stream is `3m//s` .

Explanation

To solve the problem of calculating the ratio \( t_1 : t_2 \) for a man rowing across a river, we can follow these steps:

### Step 1: Understand the Problem
We have a man rowing across a river with a speed of \( 5 \, \text{m/s} \) in still water and a river current speed of \( 3 \, \text{m/s} \). We need to find the time taken to row directly across the river (\( t_1 \)) and the time taken to row downstream the same distance (\( t_2 \)).

### Step 2: Calculate \( t_1 \)
When the man rows directly across the river, he needs to account for the current. The effective speed across the river can be calculated using the Pythagorean theorem, as he is rowing perpendicular to the flow of the river.

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