Set up the equation you would use to solve the problem. Do not actually solve the equation.

Luvenia can row 5 mph in still water. She takes as long to row 9 mi upstream as 22 mi downstream. How fast is the​ current? (Let xequalsspeed of the​ current.)

1 answer

Let \( x \) represent the speed of the current in miles per hour.

When Luvenia is rowing upstream, her effective speed is \( 5 - x \) mph. The time taken to row 9 miles upstream can be expressed as:

\[ \text{Time upstream} = \frac{9}{5 - x} \]

When rowing downstream, her effective speed is \( 5 + x \) mph. The time taken to row 22 miles downstream can be expressed as:

\[ \text{Time downstream} = \frac{22}{5 + x} \]

According to the problem, the time taken to row upstream is equal to the time taken to row downstream. Therefore, we can set up the equation:

\[ \frac{9}{5 - x} = \frac{22}{5 + x} \]

This is the equation you would use to solve for the speed of the current \( x \).