excellent PS - Manhattan GMAT mock

[myselfhari]

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

[ronnie1985]

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.

[GMATGuruNY]

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

Check here for a solution that simplifies the math and speeds up the process a bit:

https://www.beatthegmat.com/work-rate-pr ... 69024.html