A boat has a speed of 15 mph in calm water. It takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream. Which equation can be used to find c, the speed of the current?

Question

whpalmer4 · Answer

We know that the distance formula is $$d = st$$ where $d$ is distance, $s$ is speed, and $t$ is time

If the boat has a speed of $s_{boat} = 15 \text{ miles/hour}$ in still water, and the current has a speed of $c \text{ miles/hour}$, when traveling with the current, the boat will have an overall speed of $s_{boat} + c$.  Traveling against the current, the boat will have an overall speed of $s_{boat} -c $.

We don't know the distance, but we don't have to — it's the same in each direction.

Upstream                         Downstream
$$3\text{ hours} * (s_{boat} - c) =    2 \text{ hours} * (s_{boat} + c)$$
Solve that equation for $c$ and plug in your value for $s_{boat}$ to find the speed of the current.