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

We have rest of the Distance and speed and time, but not enough information to get the length of the track

(2) y = 400 meters

We have rest of the Distance and speed and time, but not enough information to get the length of the track


(1)(2)

Even with (1) and (2) we have 2 possibilities of encounter, that the faster one reach the slower one before the second lap, or after it, so not sufficient.

E) is the answer.

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Without knowing the cyclists' speed, not even relative speed, we would need both x and y to calculate the distance of the track.

Answer:C

I am taking a guess.

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To calculate distance between them we need to calculate exact speed of cyclist as time consumed by both is same whenever they meet.

Statement 1) x = 720 meters.

From this we can not calculate speed of cyclist.

Statement 2) y = 400 meters.

Again we can not calculate speed of cyclist.

Combining together also we can calculate speed of trains.

IMO Answer is E

Correct answer is E because we dont know the time nor the speed. We need more data to find the lenght of the track.

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E should be the correct answer option

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(1) x = 720 meters

INSUFFICIENT as we don't know what is the remaining length of the track

(2) y = 400 meters

INSUFFICIENT as we don't know what is the remaining length of the track

Tanking St1 and St 2 together,

INSUFFICIENT as we don't know how much is the distance between x and y

Answer is E

D

Both are sufficient.

Use speed = d/t

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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?

rate of A > rate of B

(A+B)t1=x
(A+B)t2=x


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

Did not have the time to explain 1 minute left for the competition to end

Answer is C

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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

Using both the information it is not possible to determine the length of the track; as the speeds are not given.
Hence E is the correct answer

x = 720 meters not sufficient
(2) y = 400 meters not sufficient

Both sufficient ...C
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Answer choice E. Not enough information to calculate the length.

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let faster speed be m and slower be n
let total distance be D
stmt 1 gives distance from n side when they meet 1st time
so time t is same so
720/n=D-720/m
not sufficient

stmt 2 not sufficient
y is distance when they meet 2nd time
D+D-400/m=D+400/n

using 1 and 2 and equating for m/n we get D-720/720=2D-400/D+400

so option C is correct

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t is same in both cases

1) x=720m
730/a = (d-720)/b

720b= ad- 720a
Not sufficient

2) y= 400m
(d-400)/b = 400/a

ad-400a = 400b
Not sufficient

On solving both we find a= -b

We can substitute in 1st equation to find the value of d.

IMO C

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Given: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.

Asked:What is the length of the track?

Let us assume length of the track to be x meters
The ratio of speed of fast cyclist to the speed of slow cyclist = (D-x)/x = (2D-y)/(D-y)
D^2-(3x+y)D+2xy=0

(1) x = 720 meters
Since y is unknown
NOT SUFFICIENT

(2) y = 400 meters
Since x is unknown
NOT SUFFICIENT

(1)+(2)
(1) x = 720 meters
(2) y = 400 meters
D^2-2560D+576000=0
D=2280 m
SUFFICIENT

IMO C

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No distances or speed given. Straight E.
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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

Total distance of the track is not provided. Also, it is not provided that when the meet for the second time, the slower cyclist has completed one lap or not.

Therefore, can not be determined. Answer is E

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