Circular track

[mysseo]

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. 4pai - 1.6
B. 4pai + 8.4
C. 4pai + 10.4
D. 2pai - 1.6
E. 2pai - 0.8

This is 700-800 question. Difficult..

[GmatMathPro]

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. 4pai - 1.6
B. 4pai + 8.4
C. 4pai + 10.4
D. 2pai - 1.6
E. 2pai - 0.8

This is 700-800 question. Difficult..

Using d=rt,

Let t=car B's time

Car A doesn't start for ten hours after B starts, so car A's time=t-10

Car B's rate is 2, and Car A's rate is 3.

Car B: d1=2t

Car A: d2=3(t-10)

Note that when the cars meet, their combined distances traveled must equal the circumference of the track. The circumference is 2*pi*r=20*pi. Then they have to put an additional 12 miles between them, so their total combined distances traveled is 20*pi+12:

d1+d2=20*pi+12

2t+3(t-10)=20*pi+12

2t+3t-30=20*pi+12

5t=20*pi+42

t=4*pi+8.4

Ans:

B

[Anurag@Gurome]

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. 4pai - 1.6
B. 4pai + 8.4
C. 4pai + 10.4
D. 2pai - 1.6
E. 2pai - 0.8

This is 700-800 question. Difficult..

The circumference of the circular track = 2*Ï€*10 = 20Ï€ miles

Let us start our analysis from the point when car A starts its journey.
At that time B has already covered (2*10) = 20 miles
Hence, distance between A and B = (20Ï€ - 20) miles

As A and B are moving towards each other, their relative speed = (2 + 3) = 5 mph

Hence, time required to cover the distance between them and 12 more miles = [(20Ï€ - 20) + 12]/5 = (20Ï€ - 8)/5 = (4Ï€ - 1.6) hours

Hence, B is traveling for (4Ï€ - 1.6) + 10 = [spoiler](4Ï€ + 8.4)[/spoiler] hours

The correct answer is B.

[GMATGuruNY]

Ballparking makes this problem a bit easier. Check my post here:

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

[mysseo]

Thank you all. The different approaches, but the same result made me understand the question fully.

[ArunangsuSahu]

B alone travelled = 10 hrs and 20 miles

The time A has started traveling the distance between them = 20pi-20

Relative Speed of And B=(3+2)= 5 miles/hr

so total time for B= 10+(20pi-20+12)/5-4pi+8.4