SOLUTION: A boat traveled 280 miles downstream and back. The trip downstream took 14 hours. The trip back took 140 hours. Find the speed of the boat in still water and the speed of the curre

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Question 1202398: A boat traveled 280 miles downstream and back. The trip downstream took 14 hours. The trip back took 140 hours. Find the speed of the boat in still water and the speed of the current.
Found 3 solutions by math_helper, mananth, josgarithmetic:
Answer by math_helper(2461) About Me  (Show Source):
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Downstream:  V = v + c  

    where 

        V = total speed, 

        v = speed of boat in still water, and

        c = speed of current



  V = 280mi/14hr = 20mi/hr   



This tells us

   v + c = 20      (1)





For the upstream direction, we subtract the speed of the current:

   v - c = 280/140

   v - c = 2       (2)





Add (1) and (2):  2v = 22 -->  v = 11  -->  c = 9 (plug v=11 into (1) or (2))



Ans:

  Speed of boat in still water is   11mi/hr

  Speed of current is                9mi/hr





This solution does make the assumption that the speed of the boat and the speed of the current add / subtract in a straightforward (linear) manner.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

Let boat speed =x mph in still water
Let current speed =y mph
against current x-y time taken 140.00 hours
with wind x+y time taken 14.00 hours

Distance = same= 140 miles
t=d/r
Upstream time equation

140 / ( x - y )= 140.00
Downstream time equation
140.00 /( x + 1 y) = 14.00
x 1y = 1.00 ....................1
140 / ( x- y )= 14.00
140 /( x - 1 y) = 14.00
x - y = 10.00 ...............2
Multiply (1) by 1.00
Multiply (2) by 1.00
we get
x + y = 1
x - y = 10
2 x = 11

/ 2

x = 5.5 mph

plug value of x in (1)

x - y = 1
5.5 - y = 1.00
-y = 1.00 -5.5
-1 y = -4.50
y = 4.5 mph
Complete by writing the answer

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
DIRECTION           SPEED       TIME    DIST.
Downstr             r+c          14      280
Upstr               r-c          140     280
TOTAL

system%28r%2Bc=20%2Cr-c=2%29

boat speed without current, 11 mph.
current's speed, 9 mph.