Car

akhp77 wrote:Source: MGMAT CAT

Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?

A: 4 π – 1.6
B: 4 π + 8.4
C: 4 π + 10.4
D: 2 π – 1.6
E: 2 π – 0.8

let us assume starting point X
radius 10 miles so length of track 2π*10=20π
now car A and car b travell in opposite direction
so relative speed 2+3=5
so they will meet first time after 4π hr at 8π away from starting point X
now car B will be travelling behind car A so in ever hour car A will go 1 mile ahead of car B as car Ais travelling at 1mph more every hour so after 12 hour car B will be 12 mile behind car A
so and its travelling 10 hrs earlier so altogether cab will travel 10 alone +4 hr alone when a will ovetrtake B and 12 hrs when a will move ahead by 12 miles
so 26

akhp77 wrote:Source: MGMAT CAT

Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?

A: 4 π – 1.6
B: 4 π + 8.4
C: 4 π + 10.4
D: 2 π – 1.6
E: 2 π – 0.8

Good question Prasad bhai!!

Concept of relative speeds in circular motion is tested here!

Track Length = 20 Pi

Distance travelled by Car B in 10 hrs = 2* 10
= 20 miles


Time taken for the two cars to meet = Initial gap/relative speed
=( 20 Pi -20)/(3+2)
T1= 4(pi -1)

Now again car B & car A moves apart 12 miles

T2 = 12/(3+2)
12/5
=2.4

We need T1+T2
4Pi-4+2.4
4pi-1.6

Pick A

@prasad bhai,,,


So many thx are pending frm u....and I havent received one frm u either!!

gmatmachoman wrote:@prasad bhai,,,


So many thx are pending frm u....and I havent received one frm u either!!

I would like to hug you.


I don't have OA to this problem. I will get it once I will complete my test.

akhp77 wrote:

gmatmachoman wrote:@prasad bhai,,,


So many thx are pending frm u....and I havent received one frm u either!!

I would like to hug you.


I don't have OA to this problem. I will get it once I will complete my test.

Thx bhai..but my answer is correct rite??

gmatmachoman wrote:
Thx bhai..but my answer is correct rite??

I hope it should be correct.

I have not seen your solution yet. I will see your solution tonight.

I got headache after maths test. I will complete rest in evening.

gmatmachoman - OA: B

akhp77 wrote:gmatmachoman - OA: B

Ohhh..so how to do that?

akhp77 wrote:Source: MGMAT CAT

Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?

A: 4 π – 1.6
B: 4 π + 8.4
C: 4 π + 10.4
D: 2 π – 1.6
E: 2 π – 0.8

OA: B

Hi,

even though this is a circular track problem, we can treat it as if it were a straight line.

First, we know that we're going to apply our basic formula: distance = rate * time

Let's calculate the distance between A and B at the start, i.e. the circumference of the track.

Circumference = 2(pi)r = 20pi

So, let's picture A and B starting at opposite ends of a road that's 20pi miles long.

B starts first at 2mph. After 10 hours, B has travelled 20 miles. So, when A starts moving, the distance between A and B is:

(20pi - 20) miles

Now A and B are both moving, directly towards each other. When two objects move directly towards (or away from) each other, we ADD their rates to get the overall rate.

Accordingly, once A and B are moving, their combined rate is 5 mph.

If the question had asked when does A meet B, we'd use r=5 and d=(20pi-20). However, this question asks about when car A has moved 12 miles past car B. So, the actual distance left to travel is:

(20pi - 20) + 12 = 20pi - 8

Finally, we have everything we need:

d = (20pi - 8)
r = 5

t = d/r = (20pi - 8)/5 = 4pi - 8/5 = 4pi - 1.6

Is 4pi - 1.6 one of the choices? Of course it is! The GMAT loves to provide answers that are the "right answer to the wrong question". Hence step 4 of the Kaplan Method for Problem Solving: always confirm that you've answered the right question.

The time we've calculated is the time since A started moving; the question asks for how long B has been moving. Since B started 10 hours before A, we have to add 10 hours:

4pi - 1.6 + 10 = 4pi + 8.4... choose (B).

Thanks a lot Stuart!!

I just forgot Car b has travelled 10 hrs..My mistake...!!

@Prasad bhai...
My method holds correct, just that add 10 to my answer..so u get 4 pi +8.4 hrs for car B

circumference of track=2*pi*r=20*pi
total distance covered by B before A starts=20mph

now A stands at =20*pi - 20 away from B.
Q asks where how much time it takes car A to cross B and be 12m away from B
total distance to be covered is 20*pi - 20+12

since car travels in opp direction their relative speed is 2+3=5mph

total time that car A has travelled (20*pi - 20+12)/5=4*pi-1.6

total time that car B has travelled 4*pi-1.6+10=4*pi+8.4

Thanks everybody for helping.



One confusion I got is that what is the significance of mph.

mph = meters per hours OR miles per hours

It is because other unit of distance is in miles OR because american uses this system.

I believe that official problem does not have such confusion.

Anybody would like to have any comment.

akhp77 wrote:Thanks everybody for helping.



One confusion I got is that what is the significance of mph.

mph = meters per hours OR miles per hours

It is because other unit of distance is in miles OR because american uses this system.

I believe that official problem does not have such confusion.

Anybody would like to have any comment.

The GMAT will never require you to convert between Imperial and Metric measures. So, if one unit is in miles, and then you see mph, it's definitely miles per hour.

I'm not sure if you'd see the abbreviation mph on the GMAT - the GMAT generally avoids abbreviations so there's no confusion.

Stuart Kovinsky wrote: The GMAT will never require you to convert between Imperial and Metric measures. So, if one unit is in miles, and then you see mph, it's definitely miles per hour.

I'm not sure if you'd see the abbreviation mph on the GMAT - the GMAT generally avoids abbreviations so there's no confusion.

Good one.
Thanks