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

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

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07 Sep 2015, 22:43
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15% (low)

Question Stats:

78% (01:33) correct 22% (01:11) wrong based on 156 sessions

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

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07 Sep 2015, 23:51
1
1
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

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

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08 Sep 2015, 01:00
2
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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08 Sep 2015, 03:32
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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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08 Sep 2015, 12:22
1
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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08 Sep 2015, 20:07
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2
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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08 Sep 2015, 21:31
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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

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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09 Sep 2015, 03:39
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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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09 Sep 2015, 04:13
1
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
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Vivian drives to her sister’s house and back. She takes the exact same  [#permalink]

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10 Sep 2015, 10:15
1
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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13 Sep 2015, 08:43
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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Re: Vivian drives to her sister’s house and back. She takes the exact same  [#permalink]

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02 Apr 2017, 12:35
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
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Re: Vivian drives to her sister’s house and back. She takes the exact same  [#permalink]

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03 Oct 2018, 10:02
Top Contributor
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

Another approach is to assign a "nice" value (one that works well with 50 mph and 70 mph) to the distance her sister's house.
So, let's say the distance is 350 miles

Average speed = (total distance traveled)/(total travel time)

TOTAL distance = 350 miles + 350 miles = 700 miles

Now let's calculate the TOTAL travel time.

time = distance/speed
So, travel time TO her sister's house = 350/50 = 7 hours
And travel time FROM her sister's house = 350/70 = 5 hours
So, TOTAL travel time = 7 hours + 5 hours = 12 hours

So, average speed = 700 miles/12 hours
= 700/12 miles per hour
= 350/6 miles per hour
= 175/3 miles per hour
= 58 1/3 miles per hour
≈ 58.3333 miles per hour

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

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03 Oct 2018, 14:01
Average speed = total distance/ total time. Distance is same for both the occasions. so lets take 350 as one way so 700 total distance.

now time = Distance/rate so Total time is 350/70 + 350/50

total distance/ total time

700/350/70 + 350/50
=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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05 Oct 2018, 15:03
Hi All,

We're told that 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 and on the trip back she drives an average speed of 70 miles per hour. We're asked for her approximate average speed for the round trip in miles per hour. This question can be solved in a couple of different ways. Sometimes the answer choices to these types of questions are 'spread out' in such a way that you can avoid almost all of the 'math' and use a 'logic shortcut' to get to the correct answer.

To start, since Vivian is driving the SAME distance in each direction, it will take her MORE time travel that distance at 50 miles/hour than it will take her to travel at 70 miles/hour. This makes this a 'Weighted Average' scenario - meaning that her average speed will be CLOSER to 50 miles/hour than it will be to 70 miles/hour. We can eliminate Answers C, D and E.

We also know that she travels at 70 miles/hour for some of the trip, so her average cannot be 50 miles/hour (logically, the speed must be greater than that), so we can eliminate Answer A. There's only one answer remaining...

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

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09 Oct 2018, 00:11
average speed = total distance/total time.
Distance one way is D , therefore both ways is D+D= 2d.
Total time, onwards = d/50, upwards= d/70,
Put them in the above equation i.e. D+D/ D/50+D/70, you will get 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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27 Feb 2019, 10:22
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.

We can let d = the distance one way and use the formula: average rate = total distance/total time:

average rate = 2d/(d/50 + d/70)

average rate = 2d/(7d/350 + 5d/350)

average rate = 2d/(12d/350)

average rate = 700d/(12d) = 58.3

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Re: Vivian drives to her sister’s house and back. She takes the exact same   [#permalink] 27 Feb 2019, 10:22
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