Need an easy method to solve this one!

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Need an easy method to solve this one!

by GmatKiss » Fri Oct 21, 2011 3:04 am
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)?

4(pi)- 1.6

4(pi)+ 8.4

4(pi)+ 10.4

2(pi)- 1.6

2(pi)- 0.8
Last edited by GmatKiss on Fri Oct 21, 2011 3:35 am, edited 1 time in total.
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by user123321 » Fri Oct 21, 2011 3:18 am
GmatKiss 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)?

4- 1.6

4+ 8.4

4+ 10.4

2- 1.6

2- 0.8
is it 4 + 10.4?

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by shankar.ashwin » Fri Oct 21, 2011 3:19 am
The circumference of the track = 2Pi(r) = 20Pi ~ 20*3 = 60

Since they travel in opposite direction, they relative speeds will be 2+3=5mph.

Now after meeting they travel an additional 12 miles, so total distance = 60+12 = 72.

Time = Distance/speed = 72/5 = 14.4 C IMO

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by GmatKiss » Fri Oct 21, 2011 3:37 am
sorry guys missed out (pi) when posting the question; accordingly edited!

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by Anurag@Gurome » Fri Oct 21, 2011 3:39 am
GmatKiss 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)?
All the answer choices are missing π in their expressions.

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 = (4Ï€ + 8.4) hours

The correct answer is B.
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by neelgandham » Fri Oct 21, 2011 3:39 am
I think the options are not what GmatKiss intended to type ?

Here is the solution:

As radius of the circular track is 10m, the circumference XPQX = 20*pi

Step 1 :

Let P be the point where B was when A started from X:
Time taken by B to reach P = 10 hours
Speed to B = 2mph
Distance covered = S*t = 20 miles

Step 2

Let Q be the point where A and B meet
Time taken = t1
Speed = 2+3 mph (Relative speed = Speed 1 + Speed 2)
Distance = xpqx - xp = 20pi -20

Time = t1 = distance /speed = (20pi-20)/5 = 4pi-4hours

Step 3

Distance = 12 miles
Say, time taken by the cars so that the distance between them is 12 miles = t2
Speed = 2+3 mph (Relative speed = Speed 1 + Speed 2)

Time = t2 = distance /speed = 12)/5 = 2.4

Total time taken by B [spoiler]= 10 + 4pi - 4 +2.4 = 4pi+8.4[/spoiler] (Option B , if that is what is it is :D)
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