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Vivian drives to her sister’s house and back. She takes the exact same

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Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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Vivian drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 50 miles per hour. On the trip back she drives an average speed of 70 miles per hour. What is her approximate average speed for the round trip in miles per hour?

A) 50
B) 58.3
C) 60
D) 61.7
E) 70


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[Reveal] Spoiler: OA

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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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New post 07 Sep 2015, 22:51
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Hi,

Option B.

Since Distance is constant and v=d/t...

Let t1 be time for towards trip and t2 for return trip.

5*t1 = 7*t2

Also distance d(constant for both the trips) = 50 * t1= 70 * t2

Average speed= (total distance/total time)= (2*d)/(t1 + t2) = 25*7/3 = 58.3

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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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New post 08 Sep 2015, 00:00
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Take the average speed formula:

2*(50*70) / (50+70) = 7000/120 = 58,33
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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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New post 08 Sep 2015, 02:32
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Solution: Let the distance b/n their houses be d.Let the time for trip out to her sisters house be t1 and for way back be t2.
Then, t1=d/50 and t2=d/70.
t1+t2 = (d/50)+(d/70)=120d/3500

Average time = Total distance/total time = 2d/t1+t2 = 2d(3500)/120d =58.3

Option B
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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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New post 08 Sep 2015, 11:22
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Distance covered = x
Since distance covered is same in both the directions, total distance covered = 2x
For 1st trip:
time t1 = x/50
For 2nd trip:
time t2 = x/70
Total time taken = t1 + t2 = (120x)/(50*70)
Average Speed = Total Distance/Total Time = 2x* (50*70)/ 120x = 58.3; Answer:B
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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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New post 08 Sep 2015, 19:07
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Option: B

Question: 2d/Tg + Tr

Tg: time going
Tr: Time returning

Method 1: Algebraic Approach
Going: 50 * (D/50) = D
Returning: 70 * (D/70) = D
2D / ((D/50) + (D/70)) = 58.3


Method 2: Plug in Numbers
Since we know that when distance is equal for two trips, rate and time are inversely proportional we can plug some smart numbers:
- Distance = 350
- Tg = 7 hours
- Tr = 5 hours
2(350) / (7 + 5) = 700/12 = 58.3


Method 3: Intuition
The average rate for the round trip must be between the 2 rates, but closer to the slower rate since this girl Vivian spent more time at a lower speed than at a faster speed. If you think about it, it´s just a weighted average concept. Hmmmm... 58.3 looks nice
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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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New post 08 Sep 2015, 20:31
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Bunuel wrote:
Vivian drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 50 miles per hour. On the trip back she drives an average speed of 70 miles per hour. What is her approximate average speed for the round trip in miles per hour?

A) 50
B) 58.3
C) 60
D) 61.7
E) 70


Kudos for a correct solution.


Another option is to use the little formula we have for average speed when distance traveled is equal at the two speeds.

Average Speed = 2ab/(a+b) = 2*50*70/(50 + 70) = 58.3

Answer (B)

Check out the discussion on this formula here: http://www.veritasprep.com/blog/2015/02 ... -the-gmat/
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Re:Vivian drives to her sister’s house and back. [#permalink]

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Bunuel wrote:
Vivian drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 50 miles per hour. On the trip back she drives an average speed of 70 miles per hour. What is her approximate average speed for the round trip in miles per hour?

A) 50
B) 58.3
C) 60
D) 61.7
E) 70


Kudos for a correct solution.


Average speed = total distance/total time
Here distance to Vivian's sister house and back is same as she Vivian takes the same route.
D = 50T1 and D=70T2

Therefore, T1 = D/50 and T2 = D/70

T1+T2 = 120d/3500

Therefore, average speed = 2d/120d/3500

=2d * 3500/120d

Answer is 58.3 Since, the options are far away we need not solve till the decimal points

So correct answer is option B
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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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Bunuel wrote:
Vivian drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 50 miles per hour. On the trip back she drives an average speed of 70 miles per hour. What is her approximate average speed for the round trip in miles per hour?

A) 50
B) 58.3
C) 60
D) 61.7
E) 70


Kudos for a correct solution.


Average Speed=Total Distance traveled/Total time taken
One way distance=d(say)
Then,
(d+d)/d/50+d/70=Avg speed
Solving for d, d=2d/12d*350
d=58.3
Answer B
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Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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Assuming distance as 350 miles.

Now applying formula - Total distance / Total Time taken

--> (350+350)/ (350/50)+(350/70)

---> 58.3 miles/hr

Option C
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Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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Bunuel wrote:
Vivian drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 50 miles per hour. On the trip back she drives an average speed of 70 miles per hour. What is her approximate average speed for the round trip in miles per hour?

A) 50
B) 58.3
C) 60
D) 61.7
E) 70


Kudos for a correct solution.


PRINCETON REVIEW OFFICIAL SOLUTION:

Does anything look tempting here? Something that seems logical, but is perhaps too good to be true? The trap answer, of course, is 60. It seems to make perfect sense — half way between 50 and 70 — but it’s just too easy. No matter how much you want to pick it, you have to tell yourself that if the problem could be solved that easily it wouldn’t be on the GMAT. So 60 is out. What else can we eliminate?

Common sense should tell you that answer can’t be 50 or 70. You can’t drive there at 50, come back at 70, and average 50 for the whole trip, for example. That makes no sense. It has to be somewhere between those numbers. Let’s look at our remaining answers, 58.3 and 61.7. One of these is closer to 50 and one is closer to 70. So apparently one of these trips — either the 50mph trip or the 70mph trip — has had a greater effect and is “pulling” the average speed closer to itself. Which one? When dealing with problems about rates, there are three parts to consider: rate, distance, and time. We know the rates here. The distance is the same for each trip. The determining factor, therefore, is time. It takes longer to make the trip at 50mph than at 70 mph, so Vivian spends more time at that speed. This means the average will be closer to 50 than 70, and the answer is B.

Another way to solve this problem is to plug a distance into the problem. Because the trip is the same distance each way it doesn’t matter what you choose — the answer will be the same no matter what. Mathematically, however, it will be much easier if you pick a number that is divisible by 50 and 70. So let’s make this a 350 mile trip. That means it will take Vivian 350 ÷ 50 = 7 hours to drive there, and 350 ÷ 70 = 5 hours to drive back. That’s a total of 12 hours to drive 700 miles. Thus, her average speed for the round trip is 700 ÷ 12 = 58.3.

Keep an eye out for answer choices that are too simple. If you remember that the GMAT is going to make you work for answers, you’ll avoid falling for the traps that ensnare so many test-takers.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Vivian drives to her sister’s house and back. She takes the exact same [#permalink]

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New post 02 Apr 2017, 11:35
Bunuel wrote:
Vivian drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 50 miles per hour. On the trip back she drives an average speed of 70 miles per hour. What is her approximate average speed for the round trip in miles per hour?

A) 50
B) 58.3
C) 60
D) 61.7
E) 70


Kudos for a correct solution.


2/[(1/50)+(1/70)]=58.3 mph
B
Re: Vivian drives to her sister’s house and back. She takes the exact same   [#permalink] 02 Apr 2017, 11:35
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