Princeton Review
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
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Vivian drives to her sister's house and back. She takes the
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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.AAPL wrote:Princeton Review
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
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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When the same distance is traveled at two different speeds, the average speed for the entire trip will be a bit LESS than the average of the two speeds.AAPL wrote:Princeton Review
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
Since (70+50)/2 = 60, the average speed for Vivian's's entire trip must be a bit less than 60.
The correct answer is B.
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Alternate way: UNITS CONTROL, one of the most powerful tools of our method!AAPL wrote:Princeton Review
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
$$? = {{{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{miles}}} \over {{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{hours}}}}$$
$$350\,\,{\rm{miles}}\,\,\left( {{\rm{arbitrary!}}} \right)\,\,\,\left\{ \matrix{
\,{\rm{out}}:\,\,350\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {50\,\,{\rm{miles}}}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\,\,\,\,\, = \,\,7\,{\rm{h}} \hfill \cr
\,{\rm{back}}:\,\,350\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {70\,\,{\rm{miles}}}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)\,\, = \,\,5\,{\rm{h}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{hours}}\,\, = \,12\,{\rm{h}}$$
Obs.: arrows indicate licit converters.
$$? = {{2 \cdot 350} \over {12}} = {{300 + 48 + 2} \over 6} = 58{1 \over 3}\,\,\,\left[ {{\rm{mph}}} \right]$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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We can let d = the distance one way and use the formula: average rate = total distance/total time:AAPL wrote:Princeton Review
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
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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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 that answer choices 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
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 that answer choices 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
