SOLUTION: A boat traveled 270 miles downstream and back. The trip downstream took 10 hours. The trip back took 30 hours. find the speed of the boat in still water and the speed of the curre
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Question 892673: A boat traveled 270 miles downstream and back. The trip downstream took 10 hours. The trip back took 30 hours. find the speed of the boat in still water and the speed of the current.
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
set x = boat speed in still water
set r = speed going downstream
set u = speed going upstream
set c = speed of the current
d = r * t
270 = r * 10
divide each side by 10
27 = r
270 = u * 30
divide each side by 30
9 = u
We have u = 9 and r = 27 and the speed going downstream is equal to
the speed of the boat in still water minus current. The speed going upstream
is equal to the speed of the boat in still water plus the current.
u = x - c
r = x + c
so
9 = x - c
27 = x + c
add the two equations above
36 = 2x
divide each side by 2
18 = x
Since 27 = x + c,
27 = 18 + c
add -18 to each side
9 = c
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