Question

A rowing team is practicing on a river. When the boat travels downstream, the current increases the speed of the boat. But when the boat travels upstream, the current decreases the speed of the boat. The team wrote a system letting s represent the speed in calm water and c represent the speed of the current. They found the solution for the system (s, c) to be (14, 6). How fast was the team traveling upstream and downstream?
A. The team traveled at 6 km per hour upstream and 14 km per hour downstream.
B. The team traveled at 14 km per hour upstream and 6 km per hour downstream.
C. The team traveled at 8 km per hour upstream and 20 km per hour downstream.
D. The team traveled at 20 km per hour upstream and 8 km per hour downstream.

Answer 1

From the question, we know that the solutions of the system $(s,c)$ is (14,6), which means the speed of the the boat in calm water, $s$, is 14$\frac{km}{h}$, and the speed of the current, $c$, is 6$\frac{km}{h}$. To summarize:
$s=14 \frac{km}{h}$ and $c=6 \frac{km}{h}$

We also know that when the boat travels downstream, the current increases the speed of the boat; therefore to find the speed of the boat traveling downstream, we just need to add the speed of the boat and the speed of the current:
$Speed_{downstream} =s+c$
$Speed _{downstream} =14 \frac{km}{h} +6 \frac{km}{h}$
$Speed_{downstream} =20 \frac{km}{h}$

Similarly, to find the the speed of the boat traveling upstream, we just need to subtract the speed of the current from the speed of the boat:
$Speed_{upstream} =s-c$
$Speed_{upstream} =14 \frac{km}{h} -6 \frac{km}{h}$
$Speed_{upstream} =8 \frac{km}{h}$

We can conclude that the correct answer is C. The team traveled at 8 km per hour upstream and 20 km per hour downstream.