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)?
4*(pi)-1.6
4*(pi)+8.4
4*(pi)+10.4
2*(pi)-1.6
2*(pi)-0.8
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myselfhari
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Circumference = 20pi mile
Distance covered in 10 hrs by A = 20 miles
Remaining distance to be covered to complete the circle = 20pi-20 miles
Time = (20pi-20)/5 hrs (5 =3+2, the rel velocity of cars)
To cover 12 more miles, time = 12/5 hr
Total = 10+(20pi-20+12)/5 = 4pi+8.4
(B) is the answer.
Distance covered in 10 hrs by A = 20 miles
Remaining distance to be covered to complete the circle = 20pi-20 miles
Time = (20pi-20)/5 hrs (5 =3+2, the rel velocity of cars)
To cover 12 more miles, time = 12/5 hr
Total = 10+(20pi-20+12)/5 = 4pi+8.4
(B) is the answer.
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Check here for a solution that simplifies the math and speeds up the process a bit:myselfhari 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)?
4*(pi)-1.6
4*(pi)+8.4
4*(pi)+10.4
2*(pi)-1.6
2*(pi)-0.8
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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].
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