Question

1. Ricki and Cleo are swimming in a race in Byron Bay. The current is 4 knots per hour west. Ricki swims north at 3 knots per hour. Cleo swims west at 2.8 knots per hour. a. Diagram the scenario below. b. Who will swim further in a 1-hour timed swim? Explain.

Answer 1

To analyze the swimming race between Ricki and Cleo in Byron Bay, we will address both parts of your question.

### a. Diagram the Scenario

1. **Current Direction**: The ocean current is moving west at 4 knots per hour.
2. **Ricki's Speed**: Ricki swims north at 3 knots per hour.
3. **Cleo's Speed**: Cleo swims west at 2.8 knots per hour.

Here's a simplified representation of the scenario described:

```
North
|
|
Ricki |
(3 knots)
|
|
|
----------------------------------
| |
| |
| | Cleo
(4 knots) Current ---> (2.8 knots)
| |
| |
-----------------------------------
West
```

### b. Who Will Swim Further in a 1-Hour Timed Swim?

**Ricki's Effective Speed**:
- Ricki is swimming north at 3 knots.
- The current does not affect her northward speed, so after 1 hour, she will cover:
\[
\text{Distance covered by Ricki} = 3 \text{ knots} \times 1 \text{ hour} = 3 \text{ nautical miles north}.
\]

**Cleo's Effective Speed**:
- Cleo swims west at 2.8 knots but is also affected by the current which is pushing her west at 4 knots.
- Therefore, Cleo's effective speed in the westward direction is:
\[
\text{Total effective west speed} = 2.8 \text{ knots (Cleo)} + 4 \text{ knots (current)} = 6.8 \text{ knots}.
\]
- After 1 hour, she will cover:
\[
\text{Distance covered by Cleo} = 6.8 \text{ knots} \times 1 \text{ hour} = 6.8 \text{ nautical miles west}.
\]

### Conclusion

- Ricki swims 3 nautical miles north.
- Cleo swims 6.8 nautical miles west.

**Ricki swims 3 nautical miles, while Cleo swims 6.8 nautical miles. Therefore, Cleo swims further in the 1-hour timed swim.**