JJ's boat will go 15 mph in still water. If he can go 12 mph downstream in the same amount of time it takes to go 9 mph upstream, what is the speed of the current?

Vb + Vc = 12.

Vb - Vc = 9.
Add the Eqs:
2Vb = 21.
Vb = 10.5 MPH.
Vc = 1.5 mph.

To find the speed of the current, we need to set up two separate equations.

Let's assume the speed of the current is "c" mph.

1. Downstream speed:
When JJ is going downstream (with the current), his effective speed is the sum of the speed of the boat (15 mph) and the speed of the current (c mph). So, his speed downstream is (15 + c) mph.

2. Upstream speed:
When JJ is going upstream (against the current), his effective speed is the difference between the speed of the boat (15 mph) and the speed of the current (c mph). So, his speed upstream is (15 - c) mph.

Now, we can set up the equation considering the time taken in both cases.

Time downstream = Time upstream

Distance downstream / Speed downstream = Distance upstream / Speed upstream

Let's assume the distance JJ travels is the same in both cases.

Now we can substitute the values:

Distance downstream / (15 + c) = Distance upstream / (15 - c)

We know that the time taken to go 12 mph downstream is the same as going 9 mph upstream.

So, we can write the equation as:

Distance / (15 + c) = Distance / (15 - c)

Cross-multiplying, we get:

Distance * (15 - c) = Distance * (15 + c)

Expanding, we have:

15 Distance - Distance c = 15 Distance + Distance c

Simplifying this equation:

- Distance c = Distance c

Since the distances are equal, the "Distance c" terms cancel out, leaving us with:

0 = 0

This implies that the equation is true for any value of Distance. Thus, we cannot determine the speed of the current based on this information alone.