Car B starts at point X and move clockwise around a circular

[BTGmoderatorLU]

Source: Manhattan Prep

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. \(4\pi-1.6\)
B. \(4\pi+8.4\)
C. \(4\pi+10.4\)
D. \(2\pi-1.6\)
E. \(2\pi-0.8\)

The OA is B

[deloitte247]

radius = 10
$$Circumference=2\pi r=\pi\cdot2\cdot r=\pi\cdot2r$$
Where 2r = Diameter ;
$$C=\pi\left(20\right)or\ 20\pi$$
Car B leaves 10 hrs before car A hence Car B have travelled the distance 2*10 = 20 miles which is in 10 hrs before car A and B reach one another they will cover distance of
$$\left(\pi20-20\right)miles$$
Rate A + Rate B = 2 miles/hr + 3 miles/hr = 5 miles/hr
$$Time=\frac{dis\tan ce}{rate\ }=\frac{\left(\pi20-20\right)}{5}=\left(\pi4-4\right)hours$$
It takes the time above for them to reach one another, so to travel past one another with distance of 12 miles. It will be
Distance = rate * time
12 = 5t ; t=12/5 = 2.4hrs
Therefore,
Car B has been on the circuit for
$$\left(\pi4-4\right)+\left(2.4\right)+10$$
$$\left(\pi4-4+12.4\right)hrs$$
$$\left(\pi+8.4\right)hrs$$
$$answer\ is\ Option\ B$$

[Scott@TargetTestPrep]

Source: Manhattan Prep

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. \(4\pi-1.6\)
B. \(4\pi+8.4\)
C. \(4\pi+10.4\)
D. \(2\pi-1.6\)
E. \(2\pi-0.8\)

The OA is B

Since the radius of the circular track is 10 miles, the circumference of the track is 20Ï€ miles. When the two cars first meet, they will have traveled a total distance equal to the circumference of the track, which is 20Ï€ miles. Since the two cars also put an additional 12 miles between them after they first passed each other, together they will have traveled 20Ï€ + 12 miles. If we let t = the number of hours car A has driven and put 12 miles between them after they first passed each other, we can create the distance equation:

2(t + 10) + 3t = 20Ï€ + 12

2t + 20 + 3t = 20Ï€ + 12

5t = 20Ï€ - 8

t = 4Ï€ - 1.6 = time for car A

Since car B started first, we add the 10 hours car B had already driven, so the total number of hours car B will have been traveling is 4Ï€ - 1.6 + 10 = 4Ï€ + 8.4.

Answer: B