HOT Competition 3 Sep/8AM: Two cyclists start moving simultaneously fr

Question

Two cyclists start moving simultaneously from opposite ends of a straight track towards each other back and forth. Cyclists' speeds are constant, but one is faster than the other. First time, the cyclists meet each other at a distance of x meters from the nearest end of the track. Second time, on the way back, they meet y meters from the other end of the track. What is the length of the track?

(1) x = 720 meters
(2) y = 400 meters

Moderator Note: Kudos are rewarded only for explanations published within 1 hour of posting

This question was provided by GMAT Club
for the Heroes of Timers Competition

M36-140

(1) x = 720 meters
(2) y = 400 meters

Kudos are rewarded only for explanations published within 1 hour of posting

M36-140

Bunuel · Accepted Answer

Official Solution:

Two cyclists start moving simultaneously from opposite ends of a straight track towards each other back and forth. Cyclists' speeds are constant, but one is faster than the other. First time, the cyclists meet each other at a distance of x meters from the nearest end of the track. Second time, on the way back, they meet y meters from the other end of the track. What is the length of the track?

(1) x = 720 meters
(2) y = 400 meters

Moderator Note: Kudos are rewarded only for explanations published within 1 hour of posting

This question was provided by GMAT Club
for the Heroes of Timers Competition

M36-140

Check the image below:

https://gmatclub.com/gmat-focus-tests/resources/import/img/M36-140.png

By the time of their first meeting, the total distance the two cyclists have covered equals to the the length of the track (check top image: A and B together covered 1 full length of the track). 
 
By the time of their second meeting, the total distance the two cyclists have covered equals to three times the length of the track (check the lower image: A and B together covered 3 full lengths of the track). 
 
Since the speeds are constant, the second meeting (after covering 3 full lengths of the track) occurs after a total time that is thrice the time for the first meeting (after covering 1 full length of the track). So, if by the time of their first meeting, cyclist A covered  x  meters, then by the time of their second meeting, cyclist A covered  3x  meters (3 times the distance in 3 times the time).
 
Now, check the lower image again, the total distance A covered ( 3x  meters), is  y  meters more than the length of the track, so the length of the track is  3x-y  meters.

So, to get the length we only need to know the values of  x  and  y , while speeds are irrelevant.
 
(1)  x = 720  meters

Not sufficient.
 
(2)  y = 400  meters

Not sufficient.
 
(1)+(2) The length of the track is  3x-y=3*720-400=1760  meters. Sufficient.

Answer: C

mSKR · Answer

1st : take t seconds

x= ut
D-x = vt
(u+v )t= D

d-x+y = ut'
x+d-y =vt'
(u+v)t' = 2D

t'= 2t

D=?

1: 
x= 720
D= (u+v)T

2 variable speed and time
not sufficient

2:y = 400 m
similarly 
speed and time are not variable

insufficient

1+2:

x= ut
720= ut

d-x+y = ut'
D-720+400 = u(2t)

D-720+400 = 2.720
D= 3.720-400 = 1760m

Hence C

avinash07 · Answer

Option C is Correct.

Let's suppose total distance is L.
When 1st time they meet.
Faster travelled F*T=L-720----(I)
Shower one =S*T=720----(II)
Deviding both we will get.
F/S=L-720/720.---(III).

Similarly in 2nd case.
F/S=(2L-400)/L+400.--+(iv)
As eqn(iii)=(iv)

So, upon solving {(L-720)/720}={(2L-400)/L+400}.

We will get L=1760.

Hence both statements require to ans.

C

Posted from my mobile device

eldorado12 · Answer

Ans: C

Let the two cyclists be A and B, where A is the faster one
Let the track length be t
So the first round distance covered by A:B = t-x:x
Similarly, the second round distance covered by A:B = 2t-y:t+y

Since the speed is constant, (t-x)/x = (2t-y)/(t+y)
To find t we need value of both x and y

Statement 1 alone is not sufficient 
Statement 2 alone is not sufficient

Both statements together will give the value of t

Posted from my mobile device

Nevernevergiveup · Answer

Two cyclists start moving simultaneously from opposite ends of a straight track towards each other back and forth. Cyclists' speeds are constant, but one is faster than the other. First time, the cyclists meet each other at a distance of x meters from the nearest end of the track. Second time, on the way back, they meet y meters from the other end of the track. What is the length of the track?

(1) x = 720 meters
(2) y = 400 meters

Moderator Note: Kudos are rewarded only for explanations published within 1 hour of posting

This question was provided by GMAT Club
for the Heroes of Timers Competition

M36-140

Let Va and Vb be speeds of A and B
Let B be faster than A
let t1 be first meeting time and 
t2 be second meeting time
Let L be total track length

(1) x = 720 meters

Va*t=720 
 Vb*t=L-720 
 \frac{Va}{Vb}=\frac{720}{(L-720)} 
we cant derive anything else so INSUFFICIENT

(2) y = 400 meters..........they can meet in two scenario

1. B reached other end and came back to meet A who is still reaching the end

we get one more equation similarly in terms of Va/Vb=L-400/2L-400

1. B reached other end and came back to meet A who is coming back after reaching the other end

we get one more equation similarly in terms of Va/Vb=L+400/2L-400

still INSUFFICIENT as we cant solve for L

combing (1) and (2) we cant solve for L

urshi · Answer

TOTAL DISTANCE - Z

(1) x = 720 meters - INSUFFICIENT

Z-720/S1 = 720/S2

S2/S1 = 720/Z-720

(2) y = 400 meters

320+Z/S1 = Z-320/S2

S2/S1 = Z-320/320+Z

INSUFFICIENT

(1) + (2) -

Z-320/320+Z = 720/Z-720

Z CAN BE FOUND OUT.

SUFFICIENT

ANSWER - C

Posted from my mobile device

ishwarSubra · Answer

Hey All, it seems to me that all the comments above explaining why (C) is the answer don't seem to be accounting for the case where the slow cyclist is so slow that they don't make it to the other end before the fast one catches up to them. Can you explain what in the question allows us to eliminate this case from consideration?

SKP220292 · Answer

I have the same doubt  Bunuel 
The question has mentioned "on their way  back"  - is that the indicator that the second meeting happens after the slow cyclist starts returning from the other end?

Bunuel · Answer

Yes.  “On their way back”  is the key phrase. It means that at the second meeting,  both cyclists have already reached the opposite ends and turned back .

If the faster cyclist caught the slower cyclist before the slower one reached the other end, the slower cyclist would still be on the original trip, not on the way back. So that case is ruled out by the wording of the question.

madsb18 · Answer

This type of question is quite easy if you know the formula. I have seen such PS questions as well. A very similar structure to the question.

length of the track = d. 
3y = d + x

I-------------y------------------x----I
A -> <-B

Lets presume, A is faster than B. They fist meet when B is at a distance x from B's end as A is faster. A would cover larger distance.

Distance covered by A and B, again when they meet is 3d. d for A, d for B and together d.

Now A's part in this 3d is 3y.

3y = d+x.

C.

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