A man can row 4½ miles per hour in still water and he finds that it takes him twice as long to row up as to row down the rivers. What is the rate of stream in miles per hour?
(A) 1½
(B) 2
(C) 2½
(D) 3
(E) 3½
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down the rivers
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sanju09
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A man can row 4½ miles per hour in still water and he finds that it takes him twice as long to row up as to row down the rivers. What is the rate of stream in miles per hour?
(A) 1½
(B) 2
(C) 2½
(D) 3
(E) 3½
__
Rate of stream = x
4.5+x =2 (4.5 -x)
3x = 4.5
x = 1.5
IMO A
_______________
(A) 1½
(B) 2
(C) 2½
(D) 3
(E) 3½
__
Rate of stream = x
4.5+x =2 (4.5 -x)
3x = 4.5
x = 1.5
IMO A
_______________
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rockeyb
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Ans Asanju09 wrote:A man can row 4½ miles per hour in still water and he finds that it takes him twice as long to row up as to row down the rivers. What is the rate of stream in miles per hour?
(A) 1½
(B) 2
(C) 2½
(D) 3
(E) 3½
Let the rate of stream = x .
speed up stream = x - 4 1/2 = x- 9/2
Speed down stream = x + 9/2
Given that time taken to travel up stream = 2 time taken to travel down stream .
Speed = distance / time
distance = constant so speed inversely proportional to time .
Therefore speed up stream = 1/2 (speed down stream )
x- 9/2 = 1/2(x+ 9/2 )
9/4 = 3/2 x
[spoiler]x = 3/2 = 1.5 miles / hr
Hence A
[/spoiler]
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harshavardhanc
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Plug-in approach not used till now. Let's see how to apply it.sanju09 wrote:A man can row 4½ miles per hour in still water and he finds that it takes him twice as long to row up as to row down the rivers. What is the rate of stream in miles per hour?
(A) 1½
(B) 2
(C) 2½
(D) 3
(E) 3½
since, distance is constant. Speed is inversely proportional to time. Hence, the speed upstream should 1/2 the speed downstream.
Hence, (boat speed + stream speed) = 2 (boat speed - stream speed)
or (4.5 + stream speed) = 2 (4.5 - stream speed)
first option : LHS 4.5+1.5 = 6
and RHS 4.5-1.5 = 3. Bulls eye!!!
Regards,
Harsha
Harsha
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GMATGuruNY
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We can plug in the answer choices, which represent the rate of the stream.sanju09 wrote:A man can row 4½ miles per hour in still water and he finds that it takes him twice as long to row up as to row down the rivers. What is the rate of stream in miles per hour?
(A) 1½
(B) 2
(C) 2½
(D) 3
(E) 3½
Since the time downstream is 1/2 the time upstream, the rate downstream must be double the rate upstream.
Answer choice C: rate of stream = 5/2.
Rate downstream = 9/2 + 5/2 = 7.
Rate upstream = 9/2 - 5/2 = 2.
7 is more than double 2.
Eliminate C.
Need a smaller answer choice.
The math in A looks easier. Let's try A.
Answer choice A: rate of stream = 3/2.
Rate downstream = 9/2 + 3/2 = 6.
Rate upstream = 9/2 - 3/2 = 3.
Success!
The correct answer is A.
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anirudhbhalotia
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why we are adding and subtracting the stream speed for downstream and upstream respectively?
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karthikpandian19
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This is what the question i had in mind, after going thru the answers.
This is one real tough word translation for me.
This is one real tough word translation for me.
anirudhbhalotia wrote:why we are adding and subtracting the stream speed for downstream and upstream respectively?
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mbaonmind
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This is a case of relative velocity(speed) here,karthikpandian19 wrote:This is what the question i had in mind, after going thru the answers.
This is one real tough word translation for me.
anirudhbhalotia wrote:why we are adding and subtracting the stream speed for downstream and upstream respectively?
When we do downstream, which means flow in direction of river relative velocity will be my velocity + stream velocity,
When we do upstream, which means flow in opposite direction of river relative velocity will be my velocity - stream velocity,
the previous post has explained the logic already so my explanation is late.karthikpandian19 wrote:This is what the question i had in mind, after going thru the answers.
This is one real tough word translation for me.
anirudhbhalotia wrote:why we are adding and subtracting the stream speed for downstream and upstream respectively?
Anyways, in general for the upstream,downstream problems the formula being used is --:downstream speed = boat's speed + speed of stream
upstream speed = boat's speed - speed of stream
I think that knowing this formula will ease the approach to the solution for this problem. Not knowing the formula might lead to a longer time since the approach will be the speed formula.
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I did this problem differently from all the answers and still got the right answer. Can an expert verify if it's a correct way?
Stream Down = x
Stream Up = 2x
Rate = 4.5
4.5 = x + 2x
4.5 = 3x
x = 4.5 / 3
x = 1.5
That gives me (A). Please determine if I'm falsely oversimplifying this.
Stream Down = x
Stream Up = 2x
Rate = 4.5
4.5 = x + 2x
4.5 = 3x
x = 4.5 / 3
x = 1.5
That gives me (A). Please determine if I'm falsely oversimplifying this.
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GMATGuruNY
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Check whether your approach works when the values are different:bigge2win wrote:I did this problem differently from all the answers and still got the right answer. Can an expert verify if it's a correct way?
Stream Down = x
Stream Up = 2x
Rate = 4.5
4.5 = x + 2x
4.5 = 3x
x = 4.5 / 3
x = 1.5
That gives me (A). Please determine if I'm falsely oversimplifying this.
A man can row 5 miles per hour in still water. It takes him 4 times as long to row up as to row down the river. What is the rate of the river in miles per hour?
(A) 1½
(B) 2
(C) 2½
(D) 3
(E) 3½
The correct answer is D.
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rajeshsinghgmat
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(A) 1 1/2
speed=distance/time
time=distance/speed
(time)*(speed)=distance
T_up=2*T_down
1/(b-w)=2/(b+w)
(b+w)/(b-w)=2
b+w=2b-2w
b=3w
w=b/3
b=4 1/2 = 9/2
w=(1/3)*(9/2)=3/2
w= 3/2 = 1 1/2
speed=distance/time
time=distance/speed
(time)*(speed)=distance
T_up=2*T_down
1/(b-w)=2/(b+w)
(b+w)/(b-w)=2
b+w=2b-2w
b=3w
w=b/3
b=4 1/2 = 9/2
w=(1/3)*(9/2)=3/2
w= 3/2 = 1 1/2
