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Greg is training for a marathon by running to and from work

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Greg is training for a marathon by running to and from work

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Greg is training for a marathon by running to and from work each day, a distance of 12 miles each way. He runs from home to work at an average speed of 6 miles per hour and returns at an average speed of 4 miles per hour. What is Greg’s average speed, in miles per hour, for the round trip?

A. 5.5
B. 5.0
C. 4.8
D. 2.5
E. 2.4

The OA is C.

Source: Princeton Review

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swerve wrote:
Greg is training for a marathon by running to and from work each day, a distance of 12 miles each way. He runs from home to work at an average speed of 6 miles per hour and returns at an average speed of 4 miles per hour. What is Greg’s average speed, in miles per hour, for the round trip?

A. 5.5
B. 5.0
C. 4.8
D. 2.5
E. 2.4

Source: Princeton Review
Let´s use UNITS CONTROL, one of the most powerful tools of our method!
$$? = {{{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{miles}}} \over {{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{hours}}}}$$
$$12\,\,{\rm{miles}}\,\,\,\,\left\{ \matrix{
\,\,{\rm{home - work}}:\,\,\,12\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {\,6\,\,{\rm{miles}}\,}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\,\,\,\, = \,\,2\,{\rm{h}} \hfill \cr
\,\,{\rm{work - home}}:\,\,\,12\,\,{\rm{miles}}\,\,\left( {{{1\,\,{\rm{h}}} \over {\,4\,\,{\rm{miles}}\,}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\, = \,\,3\,{\rm{h}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{total}}\,\,{\rm{\# }}\,\,{\rm{hours}}\,\,\, = \,\,5\,\,{\rm{h}}$$
Obs.: arrows indicate licit converters.

$$? = {{2 \cdot 12} \over 5} = {{20 + 4} \over 5} = 4{4 \over 5}\,\, = \,\,4.8\,\,\,\,\,\left[ {{\rm{mph}}} \right]$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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swerve wrote:
Greg is training for a marathon by running to and from work each day, a distance of 12 miles each way. He runs from home to work at an average speed of 6 miles per hour and returns at an average speed of 4 miles per hour. What is Greg’s average speed, in miles per hour, for the round trip?

A. 5.5
B. 5.0
C. 4.8
D. 2.5
E. 2.4
We can use the formula: average rate = total distance/total time:

average rate = 24/(12/6 + 12/3) = 24/5 = 4.8

Answer: C

_________________
Scott Woodbury-Stewart Founder and CEO

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Hi All,

We're told that Greg is training for a marathon by running to and from work each day, a distance of 12 miles each way; he runs from home to work at an average speed of 6 miles per hour and returns at an average speed of 4 miles per hour. We're asked for Greg’s average speed, in miles per hour, for the round trip. 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 Greg is running the SAME distance in each direction, it will take him MORE time travel that distance at 4 miles/hour than it will take him to travel at 6 miles/hour. This makes this a 'Weighted Average' scenario - meaning that his average speed will be CLOSER to 4 miles/hour than it will be to 6 miles/hour. We can eliminate Answers A and B.

Since his speed never drops below 4 miles/hour, there's no way for his average speed to be less than that - so we can eliminate Answers D and E. There's only one answer remaining...

Final Answer: C

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

_________________
Contact Rich at Rich.C@empowergmat.com

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