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A boat crossed a lake from North to South

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A boat crossed a lake from North to South [#permalink]

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A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?

A. 4
B. 5
C. 6
D. 7
E. 8
[Reveal] Spoiler: OA

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Re: A boat crossed a lake from North to South [#permalink]

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New post 26 Feb 2011, 19:04
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One way of solving this is:
Speed of boat on still water (lake)=4kmph
Speed upstream = 3kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 4+1 =5kmph

Ans is B

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Re: A boat crossed a lake from North to South [#permalink]

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New post 26 Feb 2011, 19:14
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Let downstream speed be v km/hr.
There are 3 distances. Let the frst be 12 km

distance............speed............time
12....................4 km/hr.........12/4 = 3hr
24....................3 km/hr..........24/3 = 8hr
24....................v km/hr..........24/v hr

Total distance / Total time = Average speed = 3.8
(12 + 24 + 24) / (3 + 8 + 24/v) = 3.8

Solving we get v = 456/91 = 5 km/hr (approx)

ajit257 wrote:
A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?

4
5
6
7
8

please can someone explain the concept behind this

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Re: A boat crossed a lake from North to South [#permalink]

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New post 26 Feb 2011, 19:20
dreambeliever cool explanation! thanks for that perspective.

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Re: A boat crossed a lake from North to South [#permalink]

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New post 26 Feb 2011, 19:23
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Another way will be:

Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed

If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D
=>5D/3.8 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)
=> 5/3.8 = 1/4 + 2/3 +2/x (div. both sides by D)
=> 1.31 = .25+.66 +2/x => 1.31-.91 =2/x => .4 = 2/x => x=5

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Re: A boat crossed a lake from North to South [#permalink]

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New post 26 Feb 2011, 21:21
Boat's speed, S = 4 km/h
Boat's speed upstream, U = 3 km/h
Boat's speed downstream, D = ? km/h

Formula:
S = \(\frac{1}{2}(U + D)\)

4 = \(\frac{1}{2}(3 + D)\)

\(D = 5 km/h\)

Ans: 5
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Re: A boat crossed a lake from North to South [#permalink]

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New post 30 May 2011, 10:20
fluke and dreambeliever. In general can we assume that the boat driver did not change speeds while transitioning from "still" to up/downstream ?

in this case specifically downstream.
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Re: A boat crossed a lake from North to South [#permalink]

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bblast wrote:
fluke and dreambeliever. In general can we assume that the boat driver did not change speeds while transitioning from "still" to up/downstream ?

in this case specifically downstream.


I don't see any need of assuming so. Do you? Upstream speed of the boat is mentioned. Had the question considered two factors, speed of the boat and speed of the stream, as two separate entities, we mostly assume boat's speed to be unchanged i.e. speed of boat in still/leveled waters as the true speed of the boat. Hope I answered your concern!!!
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Re: A boat crossed a lake from North to South [#permalink]

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New post 01 Sep 2011, 22:06
fluke and dreambeliever,
I have similar concern as bblast.
Wouldn't the answer be different if the given avg speed was 5 Km/hr?
I am sure, it would.
I think we should try to seek other ways (little bit lengthy ones) as solved above by gmat1220.
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Re: A boat crossed a lake from North to South [#permalink]

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New post 02 Nov 2011, 08:00
Thanks for the explanations. i had no clue.

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Re: A boat crossed a lake from North to South [#permalink]

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New post 02 Nov 2011, 08:21
fluke wrote:
Boat's speed, S = 4 km/h
Boat's speed upstream, U = 3 km/h
Boat's speed downstream, D = ? km/h

Formula:
S = \(\frac{1}{2}(U + D)\)

4 = \(\frac{1}{2}(3 + D)\)

\(D = 5 km/h\)

Ans: 5


I don't see how this is correct. You're not taking the average speed for the entire trip into account. Had the average trip for the entire trip was higher, the boats trip downstream would have been higher. However, according to your explanation it would remain the same.

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Re: A boat crossed a lake from North to South [#permalink]

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New post 14 Apr 2012, 18:00
Hi guys, sorry for resurrecting such and old topic, but I would like to hear your expert advice to show me what I am doing wrong. I set the following weighted average to solve it:

[4(2) + 3(4) + x(4)]/10 = 3.8; where 4 is the lake speed, 3 is the river upstream speed, x is the river downstream speed and 3.8 is the average speed. The weights are 2 for the lake and 4 for the river because the river is twice as longer than the lake.

Thanks in advance.

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Re: A boat crossed a lake from North to South [#permalink]

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New post 14 Apr 2012, 22:37
We can solve it by picking numbers without doing any algebra.

Lets assume a number multiple of 3 i.e. 12.

Total distance traveled by the boat is 12 + 24 + 24= 60 km @ average speed of 3.8km/hour or approx 15 hours taken for travelling distance of 60 km.

Two figures are given i.e. 3km/hour or 4 hour travel time for travelling 12 km north to south + 4km/hour i.e. 6 hour to travel 24 km upstream and balance is the answer i.e. 4hours + 6 hours + 5 hours = 15 hours.

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Re: A boat crossed a lake from North to South [#permalink]

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New post 31 Dec 2013, 05:49
fluke wrote:
Boat's speed, S = 4 km/h
Boat's speed upstream, U = 3 km/h
Boat's speed downstream, D = ? km/h

Formula:
S = \(\frac{1}{2}(U + D)\)

4 = \(\frac{1}{2}(3 + D)\)

\(D = 5 km/h\)

Ans: 5


Is this approach valid anyone?

Thanks
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Re: A boat crossed a lake from North to South [#permalink]

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New post 27 Aug 2017, 04:49
ajit257 wrote:
A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?

A. 4
B. 5
C. 6
D. 7
E. 8


Bunuel, Could you help with this question? Could you help to explain the theory for downstream and upstream for the boat traveling?
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Re: A boat crossed a lake from North to South [#permalink]

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New post 27 Aug 2017, 04:53
hazelnut wrote:
ajit257 wrote:
A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?

A. 4
B. 5
C. 6
D. 7
E. 8


Bunuel, Could you help with this question? Could you help to explain the theory for downstream and upstream for the boat traveling?


Ignore this question. It does not have proper wording. It was removed from GMAT Club's database long ago.
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Re: A boat crossed a lake from North to South   [#permalink] 27 Aug 2017, 04:53
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