In still water, a boat averages 18 18 miles per hour. it takes the same amount of time to travel 16 miles 16 miles downstream, with the current, as it does 8 8 miles upstream, against the current. what is the rate of the water's current?

The current is 6 miles per hour.

Let's create a few equations:

Traveling with the current:

(18 + c) * t = 16

Traveling against the current:

(18 - c) * t = 8

Let's multiply the 2nd equation by 2

(18 - c) * t*2 = 16

Now subtract the 1st equation from the equation we just doubled.

(18 - c) * t*2 = 16

(18 + c) * t = 16

(18 - c) * t*2 - (18 + c) * t = 0

Divide both sides by t

(18 - c) * 2 - (18 + c) = 0

Now solve for c

(18 - c) * 2 - (18 + c) = 0

36 - 2c - 18 - c = 0

36 - 2c - 18 - c = 0

18 - 3c = 0

18 = 3c

6 = c

So the current is 6 mph.

Let's verify that.

(18 + 6) * t = 16

24*t = 16

t = 16/24 = 2/3

(18 - 6) * t = 8

12*t = 8

t = 8/12 = 2/3

And it's verified.