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We are given the following information:

- Jesse travels 168 km south from Everglades City to a camp area in Everglades National Park.
- There is a 1 km/h current.
- The trip with the current takes 7 hours less than the return trip against the current.
- We are tasked with finding Jesse's speed in still water.

Let’s define:
- \( v \) as Jesse’s speed in still water (in km/h).
- \( d = 168 \) km as the distance.
- The speed with the current is \( v + 1 \) km/h.
- The speed against the current is \( v - 1 \) km/h.
- The time it takes Jesse to travel downstream is \( \frac{d}{v + 1} \).
- The time it takes Jesse to travel upstream is \( \frac{d}{v - 1} \).

From the problem, the time difference is 7 hours, so we set up the equation:

\[
\frac{168}{v - 1} - \frac{168}{v + 1} = 7
\]

### Solving the equation:
Multiply both sides by \( (v - 1)(v + 1) \) to eliminate the denominators:

\[
168(v + 1) - 168(v - 1) = 7(v^2 - 1)
\]

Simplify:

\[
168v + 168 - 168v + 168 = 7(v^2 - 1)
\]

\[
336 = 7(v^2 - 1)
\]

Divide both sides by 7:

\[
48 = v^2 - 1
\]

Add 1 to both sides:

\[
v^2 = 49
\]

Taking the square root of both sides:

\[
v = 7
\]

Thus, Jesse's speed in still water is **7 km/h**.

Would you like further details, or have any questions? Here are some related questions for practice:

1. How long does it take Jesse to travel downstream?
2. How long does it take Jesse to travel upstream?
3. What if the current were 2 km/h instead of 1 km/h?
4. What if the distance was 200 km instead of 168 km, keeping the current speed the same?
5. How would the equation change if the time difference was 5 hours instead of 7?

**Tip:** When dealing with problems involving currents, always set up equations carefully considering the relative speeds with and against the current.

Jesse takes a 3-day kayak trip and travels 168 km south from Everglades City to a camp area in Everglades National Park. The trip to the camp area with a 1 km/hr current takes 7 hours less time than the return against the current. Find the speed that Jesse travels in still water.

Learn how to solve a problem where Jesse kayaks 168 km with and against a 1 km/h current. The trip with the current takes 7 hours less than the return. Use algebra and quadratic equations to find Jesse's speed in still water. Suitable for high school students (Grades 9-12).

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