Question

Rick paddled up the river, spent the night camping, and and then paddled back. He spent 10 hours paddling and the campground was 24 miles away. If Rick kayaked at a speed of 5 mph, what was the speed of the current?

Short answer

The speed of current is 1 mph.

Step-by-step solution

Step 1. Given Information  

The given data is the time taken by Rick is total of 6 hours. He spent 10 hours paddling and the campground was 24 miles away and the speed was 5 mph.

Step 2. Calculation  

Let the speed of current is $rmph$

When he paddled up the river, he increases its speed, so the rate is $5+r$

When he paddled down the river, he decreases its speed, so the rate is $5-r$

Use the distance formula to complete the table below.

Type	Rate	Time	$D=Rt$
Upriver	$5+r$	$\frac{24}{5+r}$	24 miles
Downriver	$5-r$	$\frac{24}{5-r}$	24 miles

As the total time for up and back is 10 hours. So, we get,

$$\begin{gathered} \frac{24}{5+r}+\frac{24}{5-r}=10 \\ 24(5-r)+24(5+r)=10(5+r)(5-r) \\ 120-24r+120+24r=250-10r^2 \\ 240=250-10r^2 \\ 10r^2=10 \\ {r}^2=1 \\ r=\pm 1 \end{gathered}$$

Because the speed can not be negative So, we will discard the negative value.

Thus, the speed of current is 1 mph.