As Rich has suggested, the GMAT would provide answer choices:
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
Let F = the rate of the faster cyclist and S = the rate of the slower cyclist.
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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