45 minutes =  of an hour.


From the condition you have these two equations

    = u - v,   (1)

 = u + v.   (2)

The left side of the equation (1) is the speed of the boat relative the bank of the river when moving with the current, 
and it is the sum of the rate of the boat in still water and the current rate.

The left side of the equation (2) is the speed of the boat relative the bank of the river when moving against the current, 
and it is the difference of the rate of the boat in still water and the current rate.

Simplify the equations (1) and (2):

u - v = 6,     (3)
u + v = 8.     (4)

Now add the equations (3) and (4). You will get

2u = 6 + 8 = 14,  or  u =  = 7.

Thus you just found the speed of the boat in still water. It is 7 miles per hour.

Now it is easy to find the speed of current. It is

v = 8 - u = 8 - 7 = 1 miles per hour.

Check.  The boat' speed with the current is 7 + 1 = 8 mph.
        The time for the down a river trip is  =  of an hour.

        The boat' speed against the current is 7 - 1 = 6 mph.
        The time for the trip against the current  = 1 hour.

        The solution was checked and found to be correct.


Answer.  The speed of the boat in still water is 7 mph.  The speed of current is 1 mph.