Ann and Bea start at opposite sides of a CIRCULAR track

Let's first calculate the TOTAL DISTANCE traveled by Ann and Bea combined.
Let's let H = HALF the circumference of the circle.

So, when they meet for the FIRST TIME....

. . . we can see that their combined travel distance = H (halfway around the circle).


Once they meet the first time, we can see that, when they meet for the SECOND TIME....

. . . we can see that their combined travel distance = 2H (from the time they met for the FIRST time).

So, the TOTAL distance traveled = H + 2H = 3H

The TOTAL travel time is 1.5 hours (noon to 1:30 pm)

Since Ann's speed is 25 kilometers per hour, and Bea's speed is 10 kilometers per hour, their COMBINED SPEED = 25 + 10 = 35 kilometers per hour

Since distance = (rate)(time), we can write: 3H = (35)(1.5)
Evaluate: 3H = 52.5
So, H = 17.5

In other words, HALF the distance around the circle = 17.5 kilometers.

So, the circumference of the circle = (2)(17.5) = 35 kilometers

Answer:

The first meetup will actually take half the time of the second meetup. The reason is before the first meetup, both Ann and Bea were stationed on the diameter of the circle. On the case of the second meetup, they actually started from their first meeting point which will require them to travel the full distance instead of half the circle. So, It will take them exactly the double amount of time to meet again.

That being said,
The Second meetup was in 1:30h later.
So, the first meetup was at 0:30h later,
The distance traveled by both of them in half an hour was=(12.5+5)=17.5km.
Double it and you will get the answer which is 35 km

Answer is B) 35

The first time when Ann and Bea will meet is in the first half of the circle and the second time they would meet is in the second half of the circle.

For meeting in the second half both Ann and Bea will each complete the distance of half the circle and then complete part of the second half of the circle before they meet the second time.

So the Total distance traveled would be = Half Circumference by Ann + Half Circumference by Bea + (Part of Half circumference by Ann + Part of Half circumference by Bea)

Now the total distance travelled in the second half by both Ann and Bea can be combined to form half the Circumference of the circle

So the Total distance traveled would be = Half Circumference by Ann + Half Circumference by Bea + Half circumference of the circle = 1.5 * Circumference of the circle

Now Total distance is equal to distance travelled by Ann and Bea in 1.5 hrs = 25*1.5 + 10*1.5 = 1.5 * 35

1.5 * Circumference of the circle = 1.5 * 35

Circumference of the circle = 35

Answer is B) 35

D=R*T

----------

R=25+10=35km/hr
D=2(3/4 circ.)
T=1.5hr

---------

2(3/4 circ) = (35km/hr)*(1.5hr)

-or-

1.5circ = 35km/hr * 1.5hr

circ = 35km

let c=circumference
when A & B meet the second time, their combined distance=1.5c
1.5c/(25+10 kph)=1.5 hours
c=35 kilometers
B

Lets say Anna and Bea started at the same point travelling in the opposite distance.
Distance travelled by them to meet for the first time will be C where C is the circumference. ----> (1)

Now, according to question Anna and Bea start at a distance of C/2 apart travelling in the opposite direction. For their first meeting they will have to travel a distance of C/2. Once they meet, they will have to travel a distance of C to meet again i.e. their second meeting. Therefore, the total distance travelled by Anna and Bea will be 1.5C for their second meeting.

Distance = Rate * Time

Rate (Relative Rate) = 25+10 = 35
Time taken for the second meeting = 1.5 hours
Distance = 1.5C

1.5C = 35 *1.5
C = 35

Answer is 35

I used RELATIVE VELOCITY to solve this question.
So I assume that only A is moving and that B is stationary.

Therefore, A moves with (His speed + B's speed) = 25 + 10 km/h = 35 km/h

Also, since A is the only one moving we just see how many times does he go around the circular track
before he passes the 'Stationary' B twice.
We see he passes half the circumference once to meet B the 1st time, then another circumference to meet B the 2nd time.

Therefore the distance covered = 1.5 x Circumference = 1.5C

The time taken = 1200 - 1330 hrs = 1hr 30mins = 1.5hrs

Distance = Speed x Time

1.5C = 35 km/hr x 1.5hr
dividing both sides by 1.5
C = 35 km

The answer is B

Distance for the first meetup = pie * r (half circumference)
So time (t) for the first meet up = (pie * r) / 35

Distance for second meet up = 2*pie*r (full circumference)
Time taken = 1.5 - t
So 1.5 -t = (2*pie*r) / 35
Substitute (pie*r)/35 for t and solve
2*pie*r = 35

Posted from my mobile device

While travelling in opposite direction they actually travel TOWARD each other, that is why we add the speeds not subtract.

Posted from my mobile device

If you and I are 100 miles apart, and I'm walking towards you at a speed of 5 miles per hour, and you're walking towards me at a speed of 10 miles per hour, then the gap between us shrinks at a rate of 15 miles per hour (5 mph + 10 mph = 15 mph)

The same thing is happening in this question.

Does that help?


Cheers,
Brent

Hi,
Is that GMAT like problem? I mean that what is the chance that one will meet the problem with 2 moving objects on the circumference-like path on a real test? Thanks

This is a pretty tricky question, but I think it's within the scope of the GMAT.

However, given that the GMAT is computer adaptive, test-takers would only encounter a question of this difficulty if they were doing really really well.

Cheers,
Brent

To make it more tricky, an answer choice \(27.25\) could have been added.

At first glance, it seems that the total distance covered is \(2\)*Circumference (which results in the answer \(27.25\)). However, closer look reveals that the total distance covered is \(1.5\)*Circumference.
_________________

Hi All - one question.

How can we be so sure that the 2nd meeting happened at the 2nd part / lower part of circumference, what if the second meeting happened at the 1st part / upper part of circumference after passing the 2nd part / lower part of circumference ?? This is the only thing that I'm still confused.

Pls helpp...

Good question.

It doesn't really matter exactly WHERE the people meet.
We need only recognize that, when they meet for the first time, their COMBINED distance traveled = 1/2 of the circumference.
Then, when they meet for the second time, their COMBINED distance traveled (since the first meeting) = the whole circumference.

As long as we're okay with that, then the question can be solved without know the exact location of where they meet.

Does that help?

Cheers,
Brent

Thanks a lot Brent - it is clear now that it doesnt matter.

Scenario 1: if both Ann and Bea met the 2nd time at somewhere on the 2nd half of the Circle --> base scenario which we all have been discussing

Scenario 2: if both Ann and Bea met the 2nd time at somewhere on the 1nd half of the Circle, then
* Ann: completed 1 CIRCLE + a portion of half circumference
* Bea: completed a portion of half circumference
Combining both will generate the same result as scenario 1 i.e. both Anna and Bea have been completed 1 full circumference + half circumference

Correct ?

That's correct.

Cheers,
Brent

total distance by both, till they met second time= 1.5* circumference
Their relative speed= 25+10=35
total time taken= 1.5hrs
Distance= speed*time
1.5*circumference= 1.5*35
circumference=35

Given:
1. Ann and Bea are at opposite sides of a CIRCULAR track.
2. At 12:00 pm, Ann starts traveling clockwise at a constant speed of 25 kilometers per hour.
3. At the same time, Bea starts traveling counter-clockwise at a constant speed of 10 kilometers per hour.
4. At 1:30 pm that same day, Ann and Bea cross paths for the SECOND time.

Asked: What is the circumference (in kilometers) of the circular track?

Time taken to meet second time = 1.5 hours
Distance travelled = 1.5 * circumference
Speed = 35 km/hour

1.5 Circumference = 1.5 hours * 35 km/hr
Circumference = 35 km

IMO B