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# A boat travels for three hours with a current of 3 mph and

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A boat travels for three hours with a current of 3 mph and [#permalink]  24 Jul 2004, 21:33
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A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? How far did the boat travel one way?
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Re: PS-Boat Upstream and Downstream [#permalink]  24 Jul 2004, 21:50
Bhai wrote:
A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? How far did the boat travel one way?

Let velocity of boat in calm water be V
(V+3)*3 = (V-3)*4 ... same distance
Solving V= 21
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The distance travelled will always be fixed.

So distance = 3mph * 3h = 9miles

Speed will be (s+3)*3 = (s-3)*4 assuming the current does not change direction and stays constant

so S = 21mph
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Let B be the velocity of the boat and U be the velocity of the stream.

(B+U) x 3 = (B-U) x 4

(3+B) x 3 = (B-3)x 4

9+3B=4B-12

B=21

The boat travelled (21-3) x 4hrs = 72 miles one way.
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Venksune, you got the distance right... I overlooked the question when I calculated the distance travelled...
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same answers and methods as everyone else:

3(r+3)=4(r-3)
r=21
D=72
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Ans,
21mph speed.
72miles distance.

(Approach, same as adopted by others)
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Re: A boat travels for three hours with a current of 3 mph and [#permalink]  08 Apr 2013, 11:58
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Re: A boat travels for three hours with a current of 3 mph and [#permalink]  08 Apr 2013, 12:22
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Expert's post
TheNona wrote:

Let the speed in still water be x
Speed of stream = 3

So
Speed while going downstream = x+3
Time while going downstream = 3
Speed while going upstream = x-3
Time while going upstream = 4

Since distance traveled through both ways is same and time ratio being $$\frac{3}{4}$$, the speed ratio must be $$\frac{4}{3}$$

$$\frac{Speed downstream}{Speed upstream}$$ = $$\frac{4}{3}$$

$$\frac{x+3}{x-3}$$ = $$\frac{4}{3}$$ ------> 3x + 9 = 4x - 12 ----------> x=21

Speed in still water = 21

Distance = Speed X Time
Distance = (x+3)3 = 24 X 3 = 72
or
Distance = (x-3)4 = 18 X 4 = 72

Regards,

Narenn
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Re: A boat travels for three hours with a current of 3 mph and   [#permalink] 08 Apr 2013, 12:22
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