Question 957182: A cruise ship can sail 25 mph in calm water. Sailing with the Gulf Stream, the ship can sail 256 mi in the same amount of time it takes to sail 144 mi against the Gulf Stream. Find the rate of the Gulf Stream.
Found 5 solutions by lwsshak3, ikleyn, greenestamps, josgarithmetic, MathTherapy:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A cruise ship can sail 25 mph in calm water. Sailing with the Gulf Stream, the ship can sail 256 mi in the same amount of time it takes to sail 144 mi against the Gulf Stream. Find the rate of the Gulf Stream.
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let c=rate of gulf stream
25+c=rate of ship sailing with Gulf Stream
25-c=rate of ship sailing against Gulf Stream
travel time=distance/rate (same in both directions)
...
256(25-c)=144(25+c)
6400-256c=3600-144c
112c=2800
c=25
rate of gulf stream=25 mph
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
A cruise ship can sail 25 mph in calm water. Sailing with the Gulf Stream, the ship can sail 256 mi
in the same amount of time it takes to sail 144 mi against the Gulf Stream. Find the rate of the Gulf Stream.
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Calculations in the post by @lwsshak3 are incorrect due to arithmetic error.
His answer "25 mph" for the Gulf Stream rate is absurdist,
since then the cruise ship could not sail against the current.
I came to bring a correct solution.
let c = rate of gulf stream
25+c = rate of ship sailing with Gulf Stream
25-c = rate of ship sailing against Gulf Stream
travel time=distance/rate (same in both directions)
...
..
256(25-c) = 144(25+c)
6400 - 256c = 3600 + 144c
400c = 2800
c = 2800/400 = 7
rate of gulf stream = 7 mph
Solved correctly.
Answer by greenestamps(13364)  (Show Source):
You can put this solution on YOUR website!
Tutor @ikleyn sets the problem up with an equation which says the two times (distance divided by rate) are equal:
That of course is one valid way to set the problem up.
Another valid way to set the problem up is to use a proportion which says that, since the times are equal, the ratio of the distances is equal to the ratio of the speeds:
Clearly the two ways of setting up the problem lead immediately to identical calculations to get the answer -- so it is a matter of personal preference for which method to use.
Answer by josgarithmetic(39835) (Show Source):
Answer by MathTherapy(10855)  (Show Source):
You can put this solution on YOUR website!
A cruise ship can sail 25 mph in calm water. Sailing with the Gulf Stream, the ship can sail 256 mi in the same amount of time it takes to sail 144 mi against the Gulf Stream. Find the rate of the Gulf Stream.
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Let the stream's rate, be C
Then, the DOWNSTREAM rate (rate with the stream) is 25 + C, or 25 + C
Also, the UPSTREAM rate (rate against the stream) is: S - C, or 25 - C
With the DOWNSTREAM-DISTANCE being 256 mi, time the ship takes to travel said distance is: 
And, with the UPSTREAM-DISTANCE being 144 mi, time the ship takes to travel said distance is: 
As the times are the same, we get: 
144(25 + C) = 256(25 - C) ------ Cross-multiplying
9(25 + C) = 16(25 - C) ------ Dividing both sides by 8
9(25) + 9C = 16(25) - 16C
9C + 16C = 16(25) - 9(25)
25C = 7(25)
Stream's rate, or 
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