Question

Noreen can travel 8 miles upstream in the same time it takes into travel 12 miles downstream. Her boat travels 15 mph in Stillwater. What is the rate of the current

Answer 1

To find the rate of the current, we can start by defining some variables:

- Let \( c \) be the rate of the current in mph.
- The speed of Noreen's boat in still water is 15 mph.

When traveling upstream, the effective speed of the boat is \( 15 - c \) mph, and when traveling downstream, the effective speed is \( 15 + c \) mph.

Given:
- Distance upstream = 8 miles
- Distance downstream = 12 miles

According to the problem, the time taken to travel upstream is equal to the time taken to travel downstream. We can express time as:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

Setting up the equation for upstream and downstream travel, we have:

\[
\frac{8}{15 - c} = \frac{12}{15 + c}
\]

Now, we can cross-multiply to solve for \( c \):

\[
8(15 + c) = 12(15 - c)
\]

Expanding both sides gives:

\[
120 + 8c = 180 - 12c
\]

Now, we can combine like terms:

\[
8c + 12c = 180 - 120
\]
\[
20c = 60
\]

Dividing both sides by 20:

\[
c = 3
\]

Thus, the rate of the current is \( \boxed{3} \) mph.