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

Question

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

kbhave · Accepted Answer

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 )

Sent from my iPhone using  GMAT Club Forum mobile app

EgmatQuantExpert · Answer

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

wysiwyg · Answer

Hi,

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

Thanks for your help.

obliraj · Answer

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.

xalemsharan · Answer

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

exc4libur · Answer

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)

warrior1991 · Answer

yashikaaggarwal  How should one approach??

yashikaaggarwal · Answer

I guess its well stated above by experts. Alternatively, I just calculated the time taken by each to cover one lap. Time taken by X = 400/20 = 20 seconds Time taken by Y = 400/30 = 13.33 seconds X took 20second to cover one lap. Y took 13.33 seconds. So, X completes 3 rounds in a minute And Y complete 4.5 rounds. Y is having 1.5 round more than X per minute. 15 more rounds will be covered in 15/1.5 = 10 minutes.. Hopefully this will help.

Posted from my mobile device

Anu5162 · Answer

Relative speed :10
Relative distance: 400x15
Time = (400x15)/10 = 600s or 10m

Posted from my mobile device

kreel11 · Answer

Hi  Bunuel

I am still not convinced somehow that relative speeds are subtracted instead of adding..nowhere its mentioned that these entities travel independently, also its mentioned they travel in opposite directions. So ideally together they cover 400m via combined speed of 50m/s in 8 seconds..so for a gap of 15 rotations i.e. 6000m so Y has to relatively cover 15 rotations with rel speed of 50m/s the relative time taken will be 120 seconds or 2 minutes. Please clarify. Else the better method is 30t-20t=6000.

yugamjayant · Answer

I don't think this is the correct approach, velocities in opposite directions are added when two individual entities are moving in opposite direction on a circular track. If we solve this in X's frame of reference, we can assume Y to be moving with a speed of 50m/s, and the time taken would be 15*400/50, i.e 120 secs.

Kinshook · Answer

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

If the circumference of track is 400 meters, after how many minutes will Y have covered 15 more rotations than X?

Time after which robot Y will have 1 more rotation than X = 400/(30-20) = 40 seconds
Time after which robot Y will have 15 more rotation than X = 15*40 = 600 seconds = 10 minutes

IMO B

yugamjayant · Answer

After re-reading the question, I think I have grasp of the point that's causing confusion here. The direction of rotation doesn't matter here, when we add the two speeds, we inherently assume that that one robot is covering a +ve distance and another robot is covering a -ve distance similar to two particles moving in opposite directions in a straight line, however the author of the question just wants to check the absolute difference between the distances covered, and in this case subtracting the speed is perfectly acceptable.

DhanyaAbhirami · Answer

> Time for 1st meet = $\frac{400}{20+30}=8$ s
> In that time X covered 160m, Y covered 240m
> Y covered 80m = 0.2 rotation more rotation than X in 1 st meet
> Y covers 15 more rotations after 75 meets i.e. after $8	imes75=600$ s = 10 min

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards