Let  "x"  be the average speed of the boat relative to the water (usually called as a "boat speed in still water"), in miles per hour.


Then the speed of the boat downstream is (x+7) mph, and the time traveling 48 miles downstream is   hours.


     The speed of the boat   upstream is (x-4) mph, and the time traveling 48 miles   upstream is   hours.


Total time for the round trip is 16 hours (given !), which gives you the "time" equation


     +  = 16    hours.     (1)


It is your basic equation to solve.


Multiply equation  (1)  by  (x-7)*(x+7) = . You will get


    15*(x+7) + 15*(x-7) = 16*(x^2-49).



Simplify it step by step.

    15x + 15*7 + 15x - 15*49 = 16x^2 - 784

    16x^2 - 30x - 784 = 0.


Apply the quadratic formula


     =  = .


Only positive root  x =  = 8  makes sense.


Answer.  The boat speed in still water is 8 miles per hour.


CHECK.   Let's check equation (1). Its left side is

          +  =  +  = 15 + 1 = 16 hours - same as the given total time.   ! The solution is correct !