Question

A river has a current of 4 km/h. Find the rate of Jezebel in Stillwater if it travels 40 km downstream in the same time that it takes to travel 24 km upstream.

Answer 1

To find Jezebel's speed in still water, let’s denote her speed in still water as \( v \) km/h.

When Jezebel is traveling downstream, the speed of the current is added to her speed:
\[
\text{Downstream speed} = v + 4 \text{ km/h}
\]

When she is traveling upstream, the speed of the current is subtracted from her speed:
\[
\text{Upstream speed} = v - 4 \text{ km/h}
\]

We know from the problem statement that she travels 40 km downstream and 24 km upstream in the same amount of time.

Using the formula for time, which is distance divided by speed, we can set up the following equation:

For the downstream trip:
\[
\text{Time downstream} = \frac{40}{v + 4}
\]

For the upstream trip:
\[
\text{Time upstream} = \frac{24}{v - 4}
\]

Since the times are equal, we can set the two equations equal to each other:
\[
\frac{40}{v + 4} = \frac{24}{v - 4}
\]

Now, we can cross-multiply to eliminate the fractions:
\[
40(v - 4) = 24(v + 4)
\]

Expanding both sides:
\[
40v - 160 = 24v + 96
\]

Next, we can rearrange the equation to collect all terms involving \( v \) on one side and constant terms on the other:
\[
40v - 24v = 96 + 160
\]
\[
16v = 256
\]

Now, solve for \( v \):
\[
v = \frac{256}{16} = 16
\]

Thus, Jezebel's speed in still water is \( \boxed{16} \) km/h.