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To inspect a laboratory, robots X and Y start moving in opposite

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To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 18 May 2018, 20:51
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A
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E

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Question Stats:

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To inspect a laboratory, robots X and Y start moving in opposite directions along a circular path tracked around the laboratory.They begin from the same starting point, at the same time, and travel indefinitely at constant speeds.The speed of X is 20 meters per second and the speed of Y is 30 meters per second.If the circumference of track is 400 meters, after how many minutes will Y have covered 15 more rotations than X?
A. 5
B. 10
C. 15
D. 100
E. 600

Source:Experts Global

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Re: To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 18 May 2018, 21:47
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2

Solution



Given:
• X and Y move in the opposite direction, along the circular path
• They begin from the same starting point at the same time
• Speed of X = 20 m/s
• Speed of Y = 30 m/s
• Circumference of the track = 400 meters

To find:
• After how many minutes from the start, Y will cover 15 more rotations than X

Approach and Working:
The speed of X is 20 m/s and Y is 30 m/s
• Hence, in every second, Y is covering an extra distance of (30-20) m = 10 m
In 15 extra rotation, the extra distance Y needs to cover compared to X = 15 * circumference of the track = 15 * 400 m
• As in every second Y is covering an extra distance of 10 m, the time Y will take to cover extra 15 * 400 m = \(\frac{15 * 400}{10}\)seconds = 600 seconds = 10 minutes

Hence, the correct answer is option B.

Answer: B
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Re: To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 18 May 2018, 21:06
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Let time required to 15 rotations more than X be ‘t’
Now, 15 rotations = 15*400metres = 6000 metres
From given formation , as speed x time = distance
30t = 20t + 6000
t = 600
t = 600/ 60 ( to convert into minutes )
Ans : B (t= 10 mins )



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Re: To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 25 May 2018, 14:49
Hi,

As the robots are moving in opposite directions, shouldn't we sum the speeds rather than substract them ?

Thanks for your help.
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Re: To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 25 May 2018, 21:11
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Distance travelled in 1 minute:
X---> 20*60= 1200m; Y---> 30*60= 1800m;
Difference between distance traveled= 600m or 1.5 rotation
In 1 minute the robot travelled 1.5 rotation more.
So it will take 10 minutes for 15 rotations.
Answer B.
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Re: To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 26 May 2018, 08:03
Bunuel

Can you please suggest on the below query

wysiwyg wrote:
Hi,

As the robots are moving in opposite directions, shouldn't we sum the speeds rather than substract them ?

Thanks for your help.

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Re: To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 27 May 2018, 23:16
wysiwyg wrote:
Hi,

As the robots are moving in opposite directions, shouldn't we sum the speeds rather than substract them ?

Thanks for your help.



I had the same doubt! Please clarify!

Thanks.
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Re: To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 27 May 2018, 23:56
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wysiwyg wrote:
Hi,

As the robots are moving in opposite directions, shouldn't we sum the speeds rather than substract them ?

Thanks for your help.
That's a good question, the concept of adding speeds of both the entities traveling in opposite direction is applicable only when both the entities together are covering up the distance simultaneously and the time taken is calculated for the combined effort of both the entities, for example: How much time will it take for robot A and robot B to meet.
But here in our case both the entities are covering the distance (which in our case maybe be same track) and completing the revolutions at their individual speed. For best case of understanding, visualize that both the robots are covering circle A and circle B independently but both having same circumference. Or you can visualize this question this way: Think that both the robots are traversing in two parallel indefinite linear tracks at respective speeds, after how much time will robot B cover a distance of (15 rev*400) 6000m more than robot B.
I hope this helps.

Thanks and regards,
Sharan Salem
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To inspect a laboratory, robots X and Y start moving in opposite  [#permalink]

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New post 22 Nov 2019, 06:22
Adi93 wrote:
To inspect a laboratory, robots X and Y start moving in opposite directions along a circular path tracked around the laboratory.They begin from the same starting point, at the same time, and travel indefinitely at constant speeds.The speed of X is 20 meters per second and the speed of Y is 30 meters per second.If the circumference of track is 400 meters, after how many minutes will Y have covered 15 more rotations than X?
A. 5
B. 10
C. 15
D. 100
E. 600



time for y to rotate 1 time more than x: distance apart / rate (y-x) = 400/10 = 40 secs
time for y to rotate 15 times more than x: 40 secs * 15 * 1 min / 60 secs = 600/60 = 10 mins

Ans (B)
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To inspect a laboratory, robots X and Y start moving in opposite   [#permalink] 22 Nov 2019, 06:22
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