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A swimmer swims 3/5 the width of a river at one velocity, then swims the remainder of the river at half her initial velocity. What was the average speed across the river?



Answer :

olemakpadu
Let her initial velocity be U.

Let the width of the river be W.

She swims 3/5 the width of the river  at  U.

Remainder width =  (1 - 3/5) = 2/5.

She then swims 2/5 the width with velocity  U/2.


Average Speed  =  (Total Distance Traveled)  /  ( Total Time Taken).


Distance =  Speed * time

time  =  Distance /  Speed.

Time in first trip:    =    (3/5)W / U =   0.6W/U.

Time in second trip  =  (2/5)W / (U/2)  =  0.4W / 0.5 U =  0.8W/U

Total Distance Traveled =  W,  width of the river.

Average Speed  =      W  /  (0.6W/U  +  0.8W/U) =    W /  (1.4W/U)

                             =  W  *  U / 1.4W 
                              =    U/1.4
                              =  U * 10 / 14
                              =  (5/7) U.

Therefore Average speed is  (5/7) of the initial speed.


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