Question

1. in the mississippi river in new orleans, the creole queen paddleboat travels 4 miles upstream (against the current) in the same amount of time it travels 6 miles downstream (with the current). if the current of the river is 2 miles per hour, determine the speed of the creole queen in still water.

Explanation:

Step1: Define variables

Let \( x \) be the speed of the Creole Queen in still water (in miles per hour). The speed upstream (against the current) will be \( x - 2 \) (since the current slows it down by 2 mph), and the speed downstream (with the current) will be \( x + 2 \) (since the current speeds it up by 2 mph).

Step2: Use time formula

The formula for time is \( \text{time} = \frac{\text{distance}}{\text{speed}} \). The time taken to travel 4 miles upstream is \( \frac{4}{x - 2} \), and the time taken to travel 6 miles downstream is \( \frac{6}{x + 2} \). Since these times are equal, we can set up the equation:
\[
\frac{4}{x - 2} = \frac{6}{x + 2}
\]

Step3: Cross - multiply to solve the equation

Cross - multiplying gives us \( 4(x + 2)=6(x - 2) \).
Expand both sides:
\[
4x+8 = 6x - 12
\]
Subtract \( 4x \) from both sides:
\[
8=2x - 12
\]
Add 12 to both sides:
\[
2x=8 + 12
\]
\[
2x=20
\]
Divide both sides by 2:
\[
x = 10
\]

Answer:

The speed of the Creole Queen in still water is 10 miles per hour.