Question 1122280
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<pre>
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 = {{{d/((4/3))}}},       ({{4/3}}} = {{{4/3}}} hours =  1 hour and 20 minutes)
or

    u + 1.5 = {{{(3d)/4}}}.


The equation for the effective rate upstream is

    u - 1.5 = {{{d/4}}}.       


Thus you have this system of 2 equations in 2 unknowns

    u + 1.5 = {{{(3d)/4}}},     (1)

    u - 1.5 = {{{d/4}}}.       (2)


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


    1.5 - (-1.5) = {{{3d/4}}} - {{{d/4}}},    or    3 = {{{2d/4}}} = {{{d/2}}},


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


Now from eq(2),  u = {{{d/4}}} + 1.5 = {{{6/4}}} + 1.5 = 3 miles per hour.


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


<U>Check</U>.   Time to swim downstream is {{{6/(3+1.5)}}} = {{{6/4.5}}} = {{{4/3}}} hours.   ! Correct !

         Time to swim upstream   is {{{6/(3-1.5)}}} = {{{6/1.5}}} = 4 hours.    ! Correct !
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Solved.