SOLUTION: A boat traveled 465 miles downstream and back. The trip downstream took 12 hours. The trip back took 31 hours. Find the speed of the boat in still water and the speed of the curren

Let u be the speed of the boat in still water (in mph),
    v be the speed of the current.

Then these two equations are in the place


u + v = ,     (1)

u - v = .     (2)


To solve the system, add the two equations. You will get

2u =  + ,  hence,  u =  mph.

Then distract the two equations. You will get

2v =  - ,  hence,  v =  mph.

If u is the speed of the boat in still water and v be the speed of the current, then the speed of the boat traveling downstream 
is (u+v) relative to the bank of the river.

The speed of the boat traveling upstream is (u-v) relative to the bank of the river.

From the other side,  in the right side of the equation (1) is the speed of the boat traveling downstream.

 in the right side of the equation (2) is the speed of the boat traveling upstream.

So, the equations (1) and (2) are direct and literal translation of the condition to the math language.

The rest, i.e. the solution of the system itself, was explained above.