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

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A boat travels for three hours with a current of 3mph and [#permalink] New post 04 Sep 2007, 11:14
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A boat travels for three hours with a current of 3mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water?
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 [#permalink] New post 04 Sep 2007, 11:31
Upstream

R b -3

T 3

d d

Down stream


R b + 3

T 4

D d


d= 3(b-3)
d= 4(b + 3)

3b- 9 = 4b + 12

b = 21

The speed of the boat in calm water is 21.
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 [#permalink] New post 04 Sep 2007, 11:33
Simple problem

(x + 3)*3 = (x - 3) *4
x = 21
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 [#permalink] New post 04 Sep 2007, 11:34
For rate problems, it helps to write: Distance = rate * time
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 [#permalink] New post 04 Sep 2007, 14:35
let's say:
clam speed=X (m/h)
resistance (or propeller) speed of the water= Y (m/h)

if you take 3 hours at a speed 3mph while take 4 hours to get back, the first trip should be downstream:

X+Y=3 (mph)

in this trip, the distance you travel is 3 (hours)*3(mph)=9 miles

the sencond trip is upstream, the speed should be:
X-Y

the same distance takes you 4 hours, that is

9 (miles) /(X-Y)=4 (hours)


OK, lets see what we have now:

X+Y=3

9/(X-Y)=4

=> X=2.625 mile/hour


************
there is another quicker way to figure out this problem

first trip distance= 3*3=9 miles

second trip speed= 9 miles/ 4 hours=2.25 m/h

first trip speed =3 m/h

(first speed+second speed)/2=5.25/2=2.625 m/h------->because the MEAN of the two speeds (to and back) will counteract the infulence of water.


open to discuss
  [#permalink] 04 Sep 2007, 14:35
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