Manhattan Prep
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
A. R-4
B. R/(R+4)
C. R/(R-8)
D. 8/(R-8)
E. 2R - 4
The OA is C.
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Alex and Brenda both stand at point X. Alex begins to walk
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BTGmoderatorLU
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Let T the time that Alex will have been walking when Brenda has covered twice as much distance as Alex.
In T hour Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T - 1 hour, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T = R(T-1) --> 8T=RT-R --> T=R/(R-8).
Hence, C is the correct answer.
In T hour Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T - 1 hour, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*4T = R(T-1) --> 8T=RT-R --> T=R/(R-8).
Hence, C is the correct answer.
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fskilnik@GMATH
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Let´s explore a particular case, say R=9. In this case we have:BTGmoderatorLU wrote:Manhattan Prep
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
A. R-4
B. R/(R+4)
C. R/(R-8)
D. 8/(R-8)
E. 2R - 4
FOCUS: T (as a function of R=9)
Alex: 4T miles travelled after T h.
Brenda: 9(T-1) miles travelled after (T-1) h.
From the question stem, we know that: 9(T-1) = 2*4T to find T = 9 (h).
In short: when R=9, the "target" is also (by coincidence) 9.
(A) R-4 = 5 is OUT
(B) R/(R+4) = 9/13 is OUT
(C) R/(R-8) = 9 is a SURVIVOR
(D) 8/(R-8) = 8 is OUT
(E) 2R-4 = 14 is OUT
There was just one SURVIVOR, therefore this survivor must be the solution to the general case. It´s done.
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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fskilnik@GMATH
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Let´s REALLY solve the problem, using the WINNING TRIAD and UNITS CONTROL, one of the most powerful tools of our method!BTGmoderatorLU wrote:Manhattan Prep
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
A. R-4
B. R/(R+4)
C. R/(R-8)
D. 8/(R-8)
E. 2R - 4
DATA:
$${\rm{Alex}}\,\,\left( A \right)\,\,:\,\,\,{{4\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,T\,\,\,\,{\rm{h}}$$
$${\rm{Brenda}}\,\,\left( B \right)\,\,:\,\,\,{{R\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\,\,\,\,\,\,\,\left( {R > 8} \right)\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\left( {T - 1} \right)\,\,{\rm{h}}$$
FOCUS:
$${\rm{?}}\,\,\,{\rm{:}}\,\,\,\,T = f\left( R \right)$$
DATA-FOCUS CONNECTION:
$$\underbrace {\left( {T - 1} \right)\,\,{\rm{h}}\,\,\,\left( {{{R\,\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)}_{{\rm{distance}}\,\,{\rm{travelled}}\,\,{\rm{by}}\,\,B}\,\,\,\,\,\mathop = \limits^{{\rm{question}}\,\,{\rm{stem}}} \,\,\,\,\,2\,\, \cdot \,\,\,\underbrace {T\,\,{\rm{h}}\,\,\,\left( {{{4\,\,\,{\rm{miles}}} \over {1\,\,\,{\rm{h}}}}\matrix{
\nearrow \cr
\nearrow \cr
} } \right)}_{{\rm{distance}}\,\,{\rm{travelled}}\,\,{\rm{by}}\,\,A}\,\,$$
Obs.: arrows indicate licit converters.
$$\left( {T - 1} \right)R = 8T\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\,\,:\,\,\,T\left( {R - 8} \right) = R\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{R\, \ne \,8} \,\,\,\,\,\,\,\,?\,\,\,:\,\,T = {R \over {R - 8}}$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Scott@TargetTestPrep
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Let t = the number of hours Alex is walking and thus (t - 1) = the number of hours Brenda is biking. We can create the equation:BTGmoderatorLU wrote:Manhattan Prep
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
A. R-4
B. R/(R+4)
C. R/(R-8)
D. 8/(R-8)
E. 2R - 4
2(4t) = R(t - 1)
8t = Rt - R
R = Rt - 8t
R = t(R - 8)
R/(R - 8) = t
Answer: C
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Hi All,
We're told that Alex and Brenda both stand at point X, Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour - and ONE HOUR later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. We're asked, if R > 8, then which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered TWICE as much distance as Alex. This question can be solved by in a number of different ways, including by TESTing VALUES.
We're told that Alex walks 4 miles per hour and, an hour later, Brenda starts biking at R miles per hour.
Let's say that Alex walks for 2 HOURS; that would be 8 total miles. The question asks us to focus on Brenda's travel covering TWICE Alex's distance, so we can build all of our work around the two hours that Alex traveled.
Alex = 2 hours, 8 total miles
Brenda = 1 hour, 16 total miles
Although the prompt doesn't clearly state it, it asks for the total number of hours that Alex traveled at the point that Brenda had traveled twice Alex's distance. Thus, we're looking for an answer that equals 2 when R = 16.
Answer A: 12 NOT a match
Answer B: 16/20 NOT a match
Answer C: 16/8 = 2 This IS a match
Answer D: 8/8 = 1 NOT a match
Answer E: 16^2 - 4 = NOT a match
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that Alex and Brenda both stand at point X, Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour - and ONE HOUR later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. We're asked, if R > 8, then which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered TWICE as much distance as Alex. This question can be solved by in a number of different ways, including by TESTing VALUES.
We're told that Alex walks 4 miles per hour and, an hour later, Brenda starts biking at R miles per hour.
Let's say that Alex walks for 2 HOURS; that would be 8 total miles. The question asks us to focus on Brenda's travel covering TWICE Alex's distance, so we can build all of our work around the two hours that Alex traveled.
Alex = 2 hours, 8 total miles
Brenda = 1 hour, 16 total miles
Although the prompt doesn't clearly state it, it asks for the total number of hours that Alex traveled at the point that Brenda had traveled twice Alex's distance. Thus, we're looking for an answer that equals 2 when R = 16.
Answer A: 12 NOT a match
Answer B: 16/20 NOT a match
Answer C: 16/8 = 2 This IS a match
Answer D: 8/8 = 1 NOT a match
Answer E: 16^2 - 4 = NOT a match
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
