Let me see if I understand.
It took 4 hours to travel upstream. It took only 2 hours to travel downstream.
Speed upstream = speed downstream - 12
I will call the downstream speed s. So upstream speed is s-12
Traveled the same distance upstream as he did down?
If so, then he went 24 miles each way.
distance = rate * time
downstream: 24 = s * 2
upstream: 24 = (s-12) * 4
I get that s = 12 in the top equation, but I get that s = 15 in the bottom equation. Since the two equations do NOT give the same s, we have set the problem up wrong. I am wondering if he traveled different distances.
So if the distance he traveled upstream was d, then the distance he traveled downstream would be 48 - d.
That makes our two equations:
Downstream: 48-d = s * 2
Upstream: d = (s-12) * 4
These simplify to
48 = 2s + d
48 = 4s - d
Now if we solve this system of equations...
Add vertically and get
96 = 6s, so s = 16 miles per hour.
Plug this in and solve for d, and get that d = 16
Now see if it works in both equations:
48 = 2(16) + 16 YES
48 = 4(16) - 16 YES
So we have found that the distance he traveled up stream was 16 miles, and the distance he traveled downstream was (48-16) = 32 miles.
We found that his downstream speed was 16 mph, so his upstream speed would have been 4 mph.