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What should be the length of the race, if it is run on a track of 400

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Bunuel
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What should be the length of the race, if it is run on a track of 400 [#permalink] New post   06 Jan 2020, 07:59
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What should be the length of the race, if it is run on a track of 400 meters and it should end exactly on the 5th meeting of A and B, both of who run clockwise with speeds of 35 m/s and 45 m/s.

A. 7 km
B. 8 km
C. 9 km
D. 10 km
E. 12 km
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Re: What should be the length of the race, if it is run on a track of 400 [#permalink] New post   10 Jan 2020, 22:08
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Bunuel wrote:
What should be the length of the race, if it is run on a track of 400 meters and it should end exactly on the 5th meeting of A and B, both of who run clockwise with speeds of 35 m/s and 45 m/s.

A. 7 km
B. 8 km
C. 9 km
D. 10 km
E. 12 km


Both of them will first meet when B travels a round more than A (400 meters).
--> Let the distance covered by A when they first meet = d & time taken be 't'
--> \(t = \frac{d}{35}\) ....... (1)

Also, B covers 'd + 400' meters in the same time
--> \(t = \frac{(d + 400)}{45}\) ....... (2)

Using (1) & (2),
--> \(\frac{(d + 400)}{45} = \frac{d}{35}\)
--> \(35d + 35*400 = 45d\)
--> \(10d = 35*400\)
--> \(d = 35*40 = 1400\)

So, distance traveled by B at first meet = \(d + 400 = 1400 + 400 = 1800\) meters
At 5th meeting, distance traveled by B = \(5*1800 = 9000\) meters = \(9\) km

IMO Option C
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Re: What should be the length of the race, if it is run on a track of 400 [#permalink] New post   31 Mar 2020, 11:47
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Bunuel wrote:
What should be the length of the race, if it is run on a track of 400 meters and it should end exactly on the 5th meeting of A and B, both of who run clockwise with speeds of 35 m/s and 45 m/s.

A. 7 km
B. 8 km
C. 9 km
D. 10 km
E. 12 km


Asked: What should be the length of the race, if it is run on a track of 400 meters and it should end exactly on the 5th meeting of A and B, both of who run clockwise with speeds of 35 m/s and 45 m/s.

Time taken to meet each time = 400 / 10 = 40 seconds
Time taken for 5th meeting = 5*40 = 200 seconds

Length of the race = distance covered in 5th meeting = 45*200 m = 9 km

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Re: What should be the length of the race, if it is run on a track of 400 [#permalink] New post   31 Jan 2022, 16:04
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Bunuel wrote:
What should be the length of the race, if it is run on a track of 400 meters and it should end exactly on the 5th meeting of A and B, both of who run clockwise with speeds of 35 m/s and 45 m/s.

A. 7 km
B. 8 km
C. 9 km
D. 10 km
E. 12 km



We can PLUG IN THE ANSWERS, which represent the distance that B must travel to meet A five times.
When the correct answer is plugged in, B will travel five more 400-meter loops than A -- in other words, 2000 more meters than A.

Since B's rate = 45 meters per second, it is VERY likely that the correct distance in meters will be a MULTIPLE OF 45.
Only C -- 9000 meters -- is a multiple of 45.

C: 9000 meters
Since B's rate = 45 meters per second, the time for B to travel 9000 meters = \(\frac{distance}{rate} = \frac{9000}{45} = 200\) seconds.
Since A's rate = 35 meters per second, the distance traveled by A in 200 seconds = (rate)(time) = 35*200 = 7000 meters.
Success!
B travels 2000 more meters than A.

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Re: What should be the length of the race, if it is run on a track of 400 [#permalink]
31 Jan 2022, 16:04
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