SOLUTION: A boat takes 2 hours to go 50 KM from A to B down the stream. But the return journey from B to A. It take 3 hours. Find the uniform speed of the boat in still water and the unifor

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Question 567210: A boat takes 2 hours to go 50 KM from A to B down the stream. But the return journey from B to A. It take 3 hours. Find the uniform speed of the boat in still water and the uniform speed the stream. (Ans. 125/6 KM/H and 25/6 KM/H)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed =x km/h
current speed =y km/h
against current x-y 3.00 hours
with current x+y 2.00 hours

Distance = same= 50 km
t=d/r
50/(x-y )=3.00
3(x-y)= 50.00
3x-3y= 50 ....................1
50/(x+y )=2.00
2.00(x+y)=50
2.00x+2.00y=50 ...............2
Multiply (1) by 2.00
Multiply (2) by 3.00
we get
6x-6y = 100
6x+6y = 150
12x=250
/12
x = 125/6 km/h

plug value of x in (1)
3 x -3 y = 50
125/2 -3 y = 50
-3 y = 50 -125/2
-3 y = -25/2
y = 25/6 km/h
The speed of Boat = 125/6 km/h
The speed of current = 25/6 km/h
m.ananth@hotmail.ca