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It takes 3.5 hours for Mathew to row a distance of X miles

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It takes 3.5 hours for Mathew to row a distance of X miles  [#permalink]

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New post 24 Apr 2011, 13:16
3
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:48) correct 41% (01:30) wrong based on 55 sessions

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It takes 3.5 hours for Mathew to row a distance of X miles up the stream. Find his speed in still water.

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.
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Re: data sufficiency  [#permalink]

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New post 24 Apr 2011, 13:37
agdimple333 wrote:
It takes 3.5 hours for Mathew to row a distance of X miles up the stream. Find his speed in still water.

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.


Sol:
Speed of Matt in still water= \(v_m\)
Speed of Stream= \(v_s\)

As per the stem:
\(\frac{X}{v_m-v_s}=3.5\)-------1

Q: \(v_m=?\)

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

\(\frac{X}{v_m+v_s}=2.5\) -------2

Equating 1 and 2:
\(3.5(v_m-v_s)=2.5(v_m+v_s)\)
\(3.5v_m-3.5v_s=2.5v_m+2.5v_s\)
\(v_m=6v_s\)-------------3

We now know that Matt's speed is 6 times that of the speed of the stream. But, we don't know the exact value yet.
Not Sufficient.

(2) He can cover a distance of 84 miles downstream in 6 hours.

\(\frac{84}{v_m+v_s}=6\)
\(\frac{84}{6}=v_m+v_s\)
\(v_m+v_s=14\)-----------4

We know the combined speed of Matt and the stream is 14 m/h
Not Sufficient.

Combining both;

Substituting 3 in 4:

\(v_m+\frac{v_m}{6}=14\)
\(7v_m=14*6\)
\(v_m=2*6=12 m/h\)

Sufficient.

Ans: "C"
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Re: data sufficiency  [#permalink]

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New post 24 Apr 2011, 19:03
D/(V-x) = 3.5

(1) says

D/(V+x) = 2.5

Which is clearly insufficient

(2) says


84/(V+x) = 6

Which is clearly insufficient


(1) and (2) combined

D can be found, and thereafter (V-x) can be found, and finally V and x can be found.

Answer - C.
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Re: data sufficiency  [#permalink]

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New post 25 Apr 2011, 10:29
agdimple333 wrote:
It takes 3.5 hours for Mathew to row a distance of X miles up the stream. Find his speed in still water.

(1) It takes him 2.5 hours to cover the distance of X miles downstream.

(2) He can cover a distance of 84 miles downstream in 6 hours.


Speed of boat in still water is the average of Upstream speed and Downstream speed.

So, to calculate speed in still water, we will need to know both upstrem and downstrem speeds.

Statement 1: Time taken to cover distance downstream= 2.5.

There is a relationship between time and speed in Upstream/ Downstream problems. it goes:

\(
\frac{Time Taken To Cover Downstream Distance}{Time Taken To Cover Upstream Distance}
=
\frac{Upstream Speed}{Downstream Speed}
\)

So from this statement, we have: \(\frac{2.5}{3.5}= \frac{US}{DS}\) (US= upstream speed, DS=downstream speed)
It follows: \(5DS=7US\). Therefore \(US= \frac{5}{7} DS\).
Since we only have ratios and not actual values, this statement alone is insufficient.

Statement 2: We can calculate downstream speed using this information. Which equals \(\frac{84}{6}= 14mph\).

However, this doesn't give any info on the Upstream speed, so this statement alone is insufficient.

Combining (1) and (2), we can find out US= \(\frac{5}{7}*14= 10mph.\)

Now we have sufficient information to calculate speed of boat in still water: average of 10 and 14 that is 12 mph.

\(Answer : C\)
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Re: It takes 3.5 hours for Mathew to row a distance of X miles  [#permalink]

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Re: It takes 3.5 hours for Mathew to row a distance of X miles   [#permalink] 21 Oct 2018, 21:31
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