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The problem states:

"A boat covers a round trip journey between two points A and B in a river in \( T \) hours. If its speed in still water becomes 2 times, it would take \( \frac{80}{161}T \) hours for the same journey. Find the ratio of its speed in still water to the speed of the river."

Let's denote:
- \( v \) as the speed of the boat in still water,
- \( r \) as the speed of the river.

The effective speeds of the boat downstream and upstream are \( v+r \) and \( v-r \) respectively.

1. **Original Time Equation**:
   \[
   T = \frac{d}{v+r} + \frac{d}{v-r}
   \]
   where \( d \) is the distance between points A and B.

2. **New Time Equation** (Speed in still water becomes \( 2v \)):
   \[
   \frac{80}{161}T = \frac{d}{2v+r} + \frac{d}{2v-r}
   \]

### Solving the Equations:

Equating and manipulating the two time equations, we can find the ratio \( \frac{v}{r} \). Let’s calculate it.It appears that directly solving the equation provided no solutions, indicating that there might be an error in setting up the equations for direct solution, or it requires further manipulation or substitution to isolate variables effectively. Let's attempt a different approach by expressing everything in terms of the ratio \( \frac{v}{r} \).

### Reformulated Plan:
We'll express \( v \) as \( k \times r \), where \( k = \frac{v}{r} \), and then solve for \( k \) using the relation between the times.

1. Substitute \( v = kr \) into the original and new time expressions.
2. Equate the times proportionally as given by \( T \) and \( \frac{80}{161}T \).
3. Solve for \( k \).

Let's compute \( k \).It seems like I can’t do more advanced data analysis right now. Please try again later.

If you have any other questions or need clarification on different topics, feel free to ask!

Here are some related topics you might find interesting:

1. How does the current of a river affect the speed of a boat?


A boat covers a round trip journey between two points A and B in a river in T hours. If its speed in still water becomes 2 times, it would take (80/161)T hours for the same journey. Find the ratio of its speed in still water to the speed of the river.

Solve a problem involving a boat's speed in still water and river speed using time, distance, and speed relationships. Learn how to calculate the ratio of speed in still water to the speed of a river with detailed steps.

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