Two cyclists start simultaneously towards each other from cities Newtown and Oldtown, which are 28 miles apart. An hour later, they meet and keep pedaling with the same speed without stopping. The second cyclist arrives at Oldtown 35 minutes later than the first arrives at Newtown. Find the speed of the cyclist who arrives from Oldtown.
(No OA and no answer options. The book that this question was printed in didn't have either. Detailed explanations would be appreciated. Thank you)
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Two Cyclists
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Hi knight247,
This is a layered "system" question and is far more complex than you're likely to see on Test Day. Without the answer choices, you have no choice but to solve algebraically. What is the name of the book that you'r referring to? Is it actually a GMAT book or is it an algebra book?
GMAT assassins aren't born, they're made,
Rich
This is a layered "system" question and is far more complex than you're likely to see on Test Day. Without the answer choices, you have no choice but to solve algebraically. What is the name of the book that you'r referring to? Is it actually a GMAT book or is it an algebra book?
GMAT assassins aren't born, they're made,
Rich
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As Rich has suggested, the GMAT would provide answer choices:
The answer choices represent the value of F.
In 1 hour, F and S work together to travel the 28 miles between them and meet.
Thus, their combined rate is equal to 28 miles per hour:
F+S = 28.
Since F+S=28, and F>S, F>14.
Eliminate A and B.
S takes 35 more minutes than F to travel the entire 28 miles between Oldtown and Newton.
35 minutes = 7/12 hour.
To determine the value of F, we can PLUG IN THE ANSWERS.
When the correct answer choice is plugged in, the difference between S's total time and F's total time will be 7/12 hour.
Answer choice D: F=18mph, implying that S=10mph
F's total time to travel from Oldtown to Newtown = d/r = 28/18 = 14/9 hours.
S's total time to travel from Newtown to Oldtown = d/r = 28/10 hours.
Time difference = 28/10 - 14/9 ≈ 28/10 - 14/10 = 14/10 hours.
The time difference is too great.
Eliminate D.
To decrease the difference between the times, the difference between the rates must decrease.
Thus, the correct answer choice must be C (F=16mph, implying that S=12mph).
The correct answer is C.
Answer choice C: F=16mph, implying that S=12mph
F's total time to travel from Oldtown to Newtown = d/r = 28/16 = 7/4 hours.
S's total time to travel from Newtown to Oldtown = d/r = 28/12 hours.
Time difference = 28/12 - 7/4 = 28/12 - 21/12 = 7/12 hour.
Success!
Let F = the rate of the faster cyclist and S = the rate of the slower cyclist.Two cyclists start simultaneously towards each other from cities Newtown and Oldtown, which are 28 miles apart. An hour later, they meet and keep pedaling with the same speed without stopping. The second cyclist arrives at Oldtown 35 minutes later than the first arrives at Newtown. What is the speed, in miles per hour, of the cyclist who travels from Oldtown to Newtown?
10
12
16
18
20
The answer choices represent the value of F.
In 1 hour, F and S work together to travel the 28 miles between them and meet.
Thus, their combined rate is equal to 28 miles per hour:
F+S = 28.
Since F+S=28, and F>S, F>14.
Eliminate A and B.
S takes 35 more minutes than F to travel the entire 28 miles between Oldtown and Newton.
35 minutes = 7/12 hour.
To determine the value of F, we can PLUG IN THE ANSWERS.
When the correct answer choice is plugged in, the difference between S's total time and F's total time will be 7/12 hour.
Answer choice D: F=18mph, implying that S=10mph
F's total time to travel from Oldtown to Newtown = d/r = 28/18 = 14/9 hours.
S's total time to travel from Newtown to Oldtown = d/r = 28/10 hours.
Time difference = 28/10 - 14/9 ≈ 28/10 - 14/10 = 14/10 hours.
The time difference is too great.
Eliminate D.
To decrease the difference between the times, the difference between the rates must decrease.
Thus, the correct answer choice must be C (F=16mph, implying that S=12mph).
The correct answer is C.
Answer choice C: F=16mph, implying that S=12mph
F's total time to travel from Oldtown to Newtown = d/r = 28/16 = 7/4 hours.
S's total time to travel from Newtown to Oldtown = d/r = 28/12 hours.
Time difference = 28/12 - 7/4 = 28/12 - 21/12 = 7/12 hour.
Success!
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Alternative method, perhaps?
By comparing sides of similar triangles (ratio), area and other geometric facts, can anyone find a way of using the attached graph to solve this problem? I've labelled all intersections to help a writer describe their solution.
By comparing sides of similar triangles (ratio), area and other geometric facts, can anyone find a way of using the attached graph to solve this problem? I've labelled all intersections to help a writer describe their solution.
- Attachments
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- Any ideas?
