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

= 4Ï€ - 1.6 + 10 hours

[spoiler]= 4Ï€ + 8.4 hours

Pick B[/spoiler]