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The figure below represents a track with identical

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by BTGmoderatorLU » Sat Apr 06, 2019 2:54 pm

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Source: Manhattan Prep

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 wins the race by how many meters?

Image

A. \(40\) meters
B. \((40+10\pi)\) meters
C. \((40+20\pi)\) meters
D. \((20+10\pi)\) meters
E. \((20+20\pi)\) meters

The OA is B
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by Jay@ManhattanReview » Mon Apr 08, 2019 3:12 am
BTGmoderatorLU wrote:Source: Manhattan Prep

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 wins the race by how many meters?

Image

A. \(40\) meters
B. \((40+10\pi)\) meters
C. \((40+20\pi)\) meters
D. \((20+10\pi)\) meters
E. \((20+20\pi)\) meters

The OA is B
From the table, we see that Team B finished after 185 - 178 = 7 seconds of Team A. Thus, of the 42 seconds, the 4th runner ran for 42 - 7 = 35 seconds when Team A finished. Thus, Team B lost by the distance that the 4th runner completed in 7 seconds.

From the track figure, we know that the two straight lines make up 2*120 = 240 meters. The two identical semi-circular ends make one circle. The radius of the identical semi-circular ends = 1/2 of (180 - 120) = 30 meters. Thus, the length of identical semi-circular ends = 2Ï€*30 = 60Ï€ meters

Length of the track = 240 + 60Ï€

Length of the track yet to be covered by the 4th runner = (7/42)*(240 + 60Ï€) = 40 + 10Ï€ meters

The correct answer: B

Hope this helps!

-Jay
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