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Vivian drives to her sister’s house and back. She takes th

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Vivian drives to her sister’s house and back. She takes th

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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

OA B

Source: Princeton Review

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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...

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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BTGmoderatorDC 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

OA B

Source: Princeton Review
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

Answer: B

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BTGmoderatorDC 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

OA B

Source: Princeton Review
Say the one-way distance is 350 miles. I chose 350 since 350 is the LCM of 50 and 70.

Time taken for the out trip = Distance / Speed = 350 / 50 = 7 hours;
Time taken for the out trip = Distance / Speed = 350 / 70 = 5 hours

Aerage speed = Total distance / Total time = (2*350) / (7 + 5) = 58.33 miles per hour

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC 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
When the SAME DISTANCE is traveled at two different speed, the average speed for the entire trip will be just a little less than the average of the two speeds.
The reason:
The trip at the lower speed takes longer than the trip at the higher speed.
Since more time is spent at the lower speed, the average speed for the whole trip will be closer to the lower speed than to the higher speed.

Here, the average of the two speeds = (50+70)/2 = 60.
Thus, the average speed for the entire trip must be just a little less than 60.

The correct answer is B.

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BTGmoderatorDC 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

OA B

Source: Princeton Review
One 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

Answer: B

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