NYCAnalyst
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
Step by step analyzes:
B speed: \(2\) mph;
A speed: \(3\) mph (travelling in the opposite direction);
Track distance: \(2*\pi*r=20*\pi\);
What distance will cover B in 10h: \(10*2=20\) miles
Distance between B and A by the time, A starts to travel: \(20*\pi-20\)
Time needed for A and B to meet distance between them divided by the relative speed: \(\frac{20*\pi-20}{2+3}= \frac{20*\pi-20}{5}=4*\pi-4\), as they are travelling in opposite directions relative speed would be the sum of their rates;
Time needed for A to be 12 miles ahead of B: \(\frac{12}{2+3}=2.4\);
So we have three period of times:
Time before A started travelling: \(10\) hours;
Time for A and B to meet: \(4*\pi-4\) hours;
Time needed for A to be 12 miles ahead of B: \(2.4\) hours;
Total time: \(10+4*\pi-4+2.4=4*\pi+8.4\) hours.
Answer: B.
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