SOLUTION: Julie and Eric row their boat (at a constant speed) 63 miles downstream for 7 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours

Let u be the rate of the boat in a still water (at no current), in miles per hour.
Let v be the rate of the stream.


Then the rate rowing downstream is (u+v) relative to the river banks.

From the other side, this rate is  = 9 mph, according to the condition, 

It gives you your first equation

u + v = 9.    


The rate rowing upstream is (u-v) relative to the river banks.

From the other side, this rate is  = 7 mph, according to the condition, 

It gives you your second equation

u - v = 9.    


Combining equations (1) and (2) together, you get the system of two equations

u + v = 9,     (1)
u - v = 7.     (2)


To solve the system, add the equations (1) and (2). You will get

2u = 9 + 7 = 16  ====>  u =  = 8.


Thus you found that the rate of the boat in the still water is 8 miles per hour.

Then from (1), v = 9 - u = 9 - 8 = 1 mph.


Answer.  The rate of the current is 1 mile per hour.