kushal.adhia wrote:Two ants leave simultaneously from a spot on the floor. One of them crawls due north at 2 inches per second, and the other crawls due west at a rate one-third faster than the first ant's rate. Approximately how many feet apart will they be after 6 seconds?
A. 83
B. 1
C. 1.33
D. 1.67
E. 20
I chose C
Would appreciate it if someone could throw some light on why it is wrong.
Kushal
1/3 faster means a rate that is 4/3 of the slower rate. Since the slower rate is 2 inches per second, the faster rate is (4/3)*2 = 8/3 inches per second. Since the ants are traveling for the same amount of time, a rate that is 4/3 faster will result in a distance that is 4/3 of the shorter distance.
Distance north = r*t = 2*6 = 12.
Distance west = (4/3)*12 = 16.
These two distances form the legs of a right triangle. The distance between the ants is the hypotenuse. This right triangle is a multiple of a 3:4:5 triangle. 4*(3:4:5) = 12:16:20. Thus, the hypotenuse -- which is the distance between the ants -- is 20 inches. Since 12 inches = 1 foot, 20/12 = 5/3 = 1.67 feet.
The correct answer is D.
Last edited by GMATGuruNY on Mon Nov 08, 2010 12:05 pm, edited 2 times in total.
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