NYCAnalyst wrote:
Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?
A. 4pi – 1.6
B. 4pi + 8.4
C. 4pi + 10.4
D. 2pi – 1.6
E. 2pi – 0.8
Given: Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph.
Asked: If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?
Car B travels = 2*10 = 20 miles before Car A starts
Circumference of the track = \(2\pi*10 = 20\pi\) miles
Distance travelled by cars the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track) = 20\pi - 20 + 12 = 20\pi - 8 miles
Relative speed of the cars = 2 + 3 = 5 mph
Time taken by both cars= \((20\pi - 8) /5 = 4\pi - 1.6\)
Hours will Car B have been traveling =\( 4\pi - 1.6 + 10 = 4\pi + 8.4\) hours
IMO B
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