Question

A twig is floating downstream at 4 kilometers per hour. Just 3 kilometers behind it is a trout, also traveling downstream but at a rate of 11 kilometers per hour. How long will it be before the trout passes the twig?
If necessary, round your answer to the nearest minute.
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Answer 1

To solve this problem, let's first establish the relative speeds of the trout and the twig.

1. The speed of the twig is 4 kilometers per hour (km/h).
2. 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**.