Let t = the time for Steve and Bill to meet.Alphonsaj wrote:Steve & Bill leave points A and B respectively at the same time and travel towards each other on the same road. They meet at point C, between A and B and proceed towards their respective destinations. After meeting Bill, Steve takes 16 minutes more to reach his destination. After meeting Steve, Bill takes 9 minutes more to reach his destination.
How long did Steve take to travel from A to B, if they did not spend any time at point C?
A) 25 mins
B) 23 mins
C) 28 mins
D) 144 mins
E) Cannot be determined with the given data.
Let the distance = 1 mile.
Combined rate for Steve and Bill:
Since Steve and Bill together take t minutes to cover the 1 mile between them, the combined rate for Steve and Bill = 1/t.
Steve's rate:
Since Steve takes 16 more minutes after Steve and Bill meet, Steve's time to travel the entire 1 mile = t+16.
Thus, Steve's rate = 1/(t+16).
Bill's rate:
Since Bill takes 9 more minutes after Steve and Bill meet, Bill's time to travel the entire 1 mile = t+9.
Thus, Bill's rate = 1/(t+9).
Since the sum of Steve's rate and Bill's rate must be equal to their combined rate, we get:
1/(t+16) + 1/(t+9) = 1/t
[(t+9) + (t+16)] / [(t+9)(t+16)] = 1/t
(2t + 25)/(t² + 25t + 144) = 1/t
2t² + 25t = t² + 25t + 144
t² = 144
t = 12.
Thus, Steve's time to travel the entire 1 mile = t+16 = 12+16 = 28 minutes.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
