Answer:
2 mph
Step-by-step explanation:
The rate in still water is 6 mph. Let the rate of the water current be x mph.
Downstream:
Distance = 6 miles
Rate = 6 + x mph (current "helps")
t = unknown
[tex]6=(6+x)t\Rightarrow t=\dfrac{6}{6+x}[/tex]
Upstream:
Distance = 3 miles
Rate = 6 - x mph (current "interferes")
t = unknown
[tex]3=(6-x)t\Rightarrow t=\dfrac{3}{6-x}[/tex]
It takes the same amount of time to travel 6 miles downstream as 3 miles upstream, so
[tex]\dfrac{6}{6+x}=\dfrac{3}{6-x}[/tex]
Cross multiply:
[tex]6(6-x)=3(6+x)\\ \\36-6x=18+3x\\ \\36-18=3x+6x\\ \\9x=18\\ \\x=2\ mph[/tex]
