Question

What is the crews rowing rate in still water and the rate of the current?

Answer 1

Let x be the crew rowing rate and y the rate of the current.

When the boat goes downstram the rates add up, then we have:

$x+y$

Now, we know that it took 2 hours to travel 12 miles, this means that the speed is 6 miles per hour, hence we have the equation:

$x+y=6$

Now, when the boats go downstream the rate of the current substract from the rowing rate, then we have:

$x-y$

Since it took them 3 hours to travel 12 miles the speed in this case is 4 miles per hour, then we have the equation:

$x-y=4$

Then we have the system of equations:

$\begin{gathered} x+y=6 \\ x-y=4 \end{gathered}$

To solve this system we add the equation, then we get:

$\begin{gathered} 2x=10 \\ x=\frac{10}{2} \\ x=5 \end{gathered}$

now that we know the value of x we plug it on the first equation and solve for y:

$\begin{gathered} 5+y=6 \\ y=6-5 \\ y=1 \end{gathered}$

Therefore the rowing rate is 5 miles per hour and the current rate is 1 mile per hur.