Question 926695: A boat is traveling 9 miles downstream in the same time that he travels 3 miles upstream, against the river current. The speed of the river current is 6 miles per hour, what is the speed of the boat traveling in still water, or with no river current.
Im not sure how to set up the problem, if someone could explain that would be very helpful. not looking for the answer, more so how to set this word problem up.
Found 3 solutions by lwsshak3, TimothyLamb, MathTherapy:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A boat is traveling 9 miles downstream in the same time that he travels 3 miles upstream, against the river current. The speed of the river current is 6 miles per hour, what is the speed of the boat traveling in still water, or with no river current.
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let x=speed of boat in still water
x+6=speed of boat downstream
x-6=speed of boat upstream
travel time=distance/speed(same for both directions)
9x-54=3x+18
6x=72
x=12
Answer by TimothyLamb(4379)  (Show Source):
You can put this solution on YOUR website! x = speed of boat in still water
s = d/t
---
downstream:
x + 6 = 9/t
t = 9/(x + 6)
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upstream:
x - 6 = 3/t
t = 3/(x - 6)
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9/(x + 6) = 3/(x - 6)
9(x - 6) = 3(x + 6)
9x - 54 = 3x + 18
6x = 72
---
answer:
x = speed of boat in still water = 12 mph
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Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! A boat is traveling 9 miles downstream in the same time that he travels 3 miles upstream, against the river current. The speed of the river current is 6 miles per hour, what is the speed of the boat traveling in still water, or with no river current.
Im not sure how to set up the problem, if someone could explain that would be very helpful. not looking for the answer, more so how to set this word problem up.
Let average speed of boat in still water, be S
Speed of current: 6 mph
Traveling DOWNSTREAM, the boat is traveling WITH the current, thereby INCREASING its average speed in still
water. Therefore, average speed, traveling DOWNSTREAM = S + 6
Speed of current: 6 mph
Traveling UPSTREAM, the boat is traveling AGAINST the current, thereby REDUCING its average speed in still
water. Therefore, average speed, traveling UPSTREAM = S - 6
Time the boat takes to go 9 miles DOWNSTREAM:  , or 
Time the boat takes to go 3 miles UPSTREAM: , or 
Since time taken to go 9 miles DOWNSTREAM is the same time taken to go 3 miles UPSTREAM,
then we can say that: 
Solving this equation for S will result in the speed of the boat in still water
Do a check after, to make sure that the answers you got are correct!!
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