radius of track ; 10 miles so distance ; 20pi
speed of B ; 2mph in 10 hours distance covered ; 2*10; 20 miles
speed of A ; 3 mph
distance which A has to cover in 10 hours ; 20pi -20 miles
relative speed of car A & B 5 miles
time it will take to meet ; 20pi-20/5 ; 4pi-4 hrs
second part of question is put another 12 miles between them i.e A is ahead of B by 12 miles ; i.e 12/5 ; 2.4 hrs
net time ; 2.4+4pi-4+10 ;
4pi+8.4
OPTION B

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
_________________