Let u be the rate of the swimmer in still water, in miles per hour,

and let d be the distance traveled one way.


Then the effective speed (rate) of the swimmer downstream is  (u+1.5)  miles per hour, while 

     the effective speed (rate) of the swimmer upstream   is  (u-1.5)  miles per hour.


The equation for the effective rate downstream is

    u + 1.5 = ,       ({{4/3}}} =  hours =  1 hour and 20 minutes)
or

    u + 1.5 = .


The equation for the effective rate upstream is

    u - 1.5 = .       


Thus you have this system of 2 equations in 2 unknowns

    u + 1.5 = ,     (1)

    u - 1.5 = .       (2)


Subtract eq(2) from eq(1). You will get


    1.5 - (-1.5) =  - ,    or    3 =  = ,


which implies   d = 6.   Thus the one way distance is 6 miles.


Now from eq(2),  u =  + 1.5 =  + 1.5 = 3 miles per hour.


Answer.  One way distance is 6 miles.  The swimmer rate in still water is 3 miles per hour.


Check.   Time to swim downstream is  =  =  hours.   ! Correct !

         Time to swim upstream   is  =  = 4 hours.    ! Correct !