To solve this problem, let's first establish the relative speeds of the trout and the twig.
- The speed of the twig is 4 kilometers per hour (km/h).
- The speed of the trout is 11 kilometers per hour (km/h).
Next, we'll find the speed of the trout relative to the twig:
\[ \text{Relative speed} = \text{Speed of trout} - \text{Speed of twig} = 11 , \text{km/h} - 4 , \text{km/h} = 7 , \text{km/h} \]
Now, we know that the trout is 3 kilometers behind the twig. To find out how long it will take for the trout to catch up with the twig, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative speed}} \]
Substituting the distance of 3 kilometers and the relative speed of 7 km/h into the formula:
\[ \text{Time} = \frac{3 , \text{km}}{7 , \text{km/h}} = \frac{3}{7} , \text{hours} \]
To convert the time from hours to minutes:
\[ \text{Time in minutes} = \frac{3}{7} \times 60 , \text{minutes} \approx 25.71 , \text{minutes} \]
Rounding to the nearest minute, we find:
\[ \text{Time} \approx 26 , \text{minutes} \]
Thus, the trout will pass the twig in approximately 26 minutes.