SOLUTION: Traceling downstream, a boat covers a distance of 27 kilometers in 3 hrs. Traveling upstream it taks the boat twice at mush time to cover 2/3s of the dist. Find the reat of the boa

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Traceling downstream, a boat covers a distance of 27 kilometers in 3 hrs. Traveling upstream it taks the boat twice at mush time to cover 2/3s of the dist. Find the reat of the boa      Log On

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Question 16709: Traceling downstream, a boat covers a distance of 27 kilometers in 3 hrs. Traveling upstream it taks the boat twice at mush time to cover 2/3s of the dist. Find the reat of the boat in still water and the rate of the current.
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of the boat be x and the speed of the current downstream be y 

then x+y=27/3=9 km/hr [speed downstream]

then x-y=(2/3*27)/6 [two thirds of distance means 2/3 of 27 km.]
                   
 [double the time means 6 hours instead of 3]

=2*(18)/6= 6 km/hr [speed upstream]




now x+y=9
    x-y=6

2x=15 => x=7.5 km/hr [solving simueltanously]

then y=9-x=9-7.5=1.5 km/hr


Hence,speed of boat in still water will be 7.5 km/hr and rate of current is 1.5 km/hr.
Hope this helps,
Prabhat