Question

In Stillwater, above average is 6 mph. It takes the same amount of time to travel 6 miles downstream, with the current, as it is 3 miles upstream, I can see the current. What is the rate of the water is current?

Answer 1

2 mph

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

`6=(6+x)t\Rightarrow t=(6)/(6+x)`

Upstream:

Distance = 3 miles

Rate = 6 - x mph (current "interferes")

t = unknown

`3=(6-x)t\Rightarrow t=(3)/(6-x)`

It takes the same amount of time to travel 6 miles downstream as 3 miles upstream, so

`(6)/(6+x)=(3)/(6-x)`

Cross multiply:

`6(6-x)=3(6+x)\\ \\36-6x=18+3x\\ \\36-18=3x+6x\\ \\9x=18\\ \\x=2\ mph`