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06 Oct 2014, 08:47
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The figure below represents a track with identical semi-circular ends used for a 4-lap relay race involving two 4-person teams (where each team member runs one complete lap around the track). The table below shows the lap times for each runner on Team A and Team B. Assuming that each runner runs at a constant rate, Team A win the race by how many meters?
A. 40 meters
B. \((40 + 10\pi)\) meters
C. \((40 + 20\pi)\) meters
D. \((20 + 10\pi)\) meters
E. \((20 + 20\pi)\) meters
Untitled.png [ 26.39 KiB | Viewed 50522 times ]
A. 40 meters
B. \((40 + 10\pi)\) meters
C. \((40 + 20\pi)\) meters
D. \((20 + 10\pi)\) meters
E. \((20 + 20\pi)\) meters
Attachment:
Untitled.png [ 26.39 KiB | Viewed 50522 times ]
10 Oct 2014, 22:01
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\(Perimeter = 120 + 120 + 30\pi + 30\pi = 240 + 60\pi\)
Refer the modified diagram below:
Untitled.png [ 33.11 KiB | Viewed 44681 times ]
At 178 seconds, when Team A completed the race, last runner of Team B had 42-35 = 7 seconds to complete the race.
We require to find the distance covered in last 7 seconds
Distance covered in 42 seconds is \(240 + 60\pi\), so distance covered in 7 seconds
\(= \frac{7}{42} * (240 + 60\pi) = 40 + 10\pi\)
Answer = B
Refer the modified diagram below:
Attachment:
Untitled.png [ 33.11 KiB | Viewed 44681 times ]
At 178 seconds, when Team A completed the race, last runner of Team B had 42-35 = 7 seconds to complete the race.
We require to find the distance covered in last 7 seconds
Distance covered in 42 seconds is \(240 + 60\pi\), so distance covered in 7 seconds
\(= \frac{7}{42} * (240 + 60\pi) = 40 + 10\pi\)
Answer = B
06 Oct 2014, 12:01
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Bunuel
Tough and Tricky questions: Distance/Rate .
The figure below represents a track with identical semi-circular ends used for a 4-lap relay race involving two 4-person teams (where each team member runs one complete lap around the track). The table below shows the lap times for each runner on Team A and Team B. Assuming that each runner runs at a constant rate, Team A win the race by how many meters?
A. 40 meters
B. \((40 + 10\pi)\) meters
C. \((40 + 20\pi)\) meters
D. \((20 + 10\pi)\) meters
E. \((20 + 20\pi)\) meters
Attachment:
Untitled.png
radius of the curved part (semi-circle) = 1/2(60) =30
thus perimeter of the track (120*2) + 2pi(30) = 240 + 60pi
now as per the chart, team A beats team b by 7 sec. obviously, the final lap is run by the last runner of team B which takes 42 seconds to run the complete track.
during these 7 secs, this last runner would have covered 7/42 = 1/6 of the lap.
thus Team A defeated team B by 1/6(240 + 60pi) = 40 + 10 pi
hence B
