SOLUTION: a boat traveled 30 miles down stream in 3 hours and made a return trip in 5 hours. find the speed of a boat in still water and the speed of the current.

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Question 694124: a boat traveled 30 miles down stream in 3 hours and made a return trip in 5 hours. find the speed of a boat in still water and the speed of the current.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Boat speed speed =x mph
current speed =y mph
against current 5 hours
with current 3 hours

Distance with current 30 miles distance against current 30
t=d/r against current (x-y)
30.00 / ( x - y )= 5.00

5.00 x - -5.00 y = 30.00 ....................1
with current (x+y)
30.00 / ( x + y )= 3.00
3.00 ( x + y ) = 30.00
3.00 x + 3.00 y = 30.00 ...............2
Multiply (1) by 3.00
Multiply (2) by 5.00
we get y
15.00 x + -15.00 y = 90.00
15.00 x + 15.00 = 150.00
30.00 x = 240.00
/ 30.00
x = 8 mph

plug value of x in (1) y
5 x -5 y = 30
40 -5 -40 = 30
-5 y = 30
-5 y = -10 mph
y = 2
Boat speed 8 mph
current 2 mph

CHECK
x+y= 10
X-y= 6 +
30.00 / ( 10.00 )= 3
30 / ( 6 ) = 5