clockwise....

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

π ≈ 3.

Car B is traveling for more than 10 hours, so answer choices D and E are too small, and A is unlikely. The correct answer is either B or C.

Circumference of track = 20π ≈ 60 miles.
In 10 hours, distance for B = 2*10 = 20 miles.
60-20 = 40 miles between A and B.
A and B now have to travel the 40 miles between them and then -- after they meet -- keep traveling in opposite directions until there is another 12 miles between them. So the total distance that they need to travel is 40+12 = 52 miles.
When things work together, we can add their rates. Combined rate for A+B = 3+2 = 5 miles/hour.
Time for A+B = Distance/Rate = 52/5 = 10.4 hours.
Since B traveled for 10 hours before A joined in, the total time for B = 10 + 10.4 = 20.4 hours.
Only answer choice B works: 4π + 8.4 ≈ 12 + 8.4 = 20.4.

The correct answer is B

j_shreyans 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)4pie – 1.6

B)4pie + 8.4

C)4pie + 10.4

D)2pie – 1.6

E)2pie – 0.8

OAB

The total length of the track is 20π miles. In 10 hours, Car B would’ve moved 20 miles along the track leaving a distance of 20π - 20 miles between the two cars. At this point, both cars are in motion towards each other and their purpose is to first finish 20π - 20 miles between them, which would take them (20π – 20)/(2 + 3) = 4π – 4 hours plus the time that would take them 12 miles apart, which is 12/5 hours. Hence, total time = 4π – 4 + 2.4 hours = 4π – 1.6 hours. Since Car B has already travelled for 10 hours, hence Car B’s total travel time at this point is

= 4π – 1.6 + 10 hours

[spoiler]= 4π + 8.4 hours

Pick B[/spoiler]