karthikpandian19 wrote:A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10 th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30 th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Let A = A's rate and B = B's rate.
A gives B a head start of 48 meters:
After the head start, the distance traveled by B = 480-48 = 432 meters.
A travels the entire distance.
Time for A to travel 480 meters = 480/A.
Time for B to travel 432 meters = 432/B.
A wins by 1/10 of a minute = 6 seconds.
In other words, the difference between B's time and A's time is 6 seconds:
432/B - 480/A = 6.
A gives B a head start of 144 meters:
After the head start, the distance traveled by B = 480-144 = 336 meters.
A travels the entire distance.
Time for A to travel 480 meters = 480/A.
Time for B to travel 336 meters = 336/B.
B wins by 1/30 of a minute = 2 seconds.
In other words, the difference between A's time and B's time is 2 seconds:
480/A - 336/B = 2.
Adding the two equations, we get:
(432/B - 480/A) + (480/A - 336/B) = 6+2
96/B = 8
B = 12.
The correct answer is
A.
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
