Hi Amanda.

Let b = the speed of the boat relative to still water. This is the constant speed you are trying to find. Then b - 4 is its speed going upstream and b + 4 is its speed returning downstream.

Let t = the time it takes to get to the far point where the boat turns around. Then 12 - t = the time it takes for it to return (because the total time is 12 hours).

Now we know that speed = distance / time. So we can write the two legs of the journey as follows:

Upstream: (b - 4) = 24 / t
Downstream: (b + 4) = 24 / (12 - t)

So we have two equations with two unknown variables t and b. Since we really only care about b, we should solve one of the equations for t and then substitute. Let's use the upstream equation:

(b - 4) = 24 / t
t = 24 / (b - 4)

Next, substitute this expression for t into the second equation wherever you see t:

(b + 4) = 24 / (12 - t)
(b + 4) = 24 / (12 - (24 / (b - 4)) )

Can you solve the equation for b now?
Stephen La Rocque.