"A" and "B" run around a circular track

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue May 22, 2018 1:30 pm

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"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap?

A. 90 seconds
B. 54.44 seconds
C. 110 seconds
D. 63 seconds
E. 77 seconds

The OA is A.

Please, can anyone explain how can I solve this PS question? I'm confused that how can A meets B for the first time in the middle of 5th lap since its a circle. Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Tue May 22, 2018 1:30 pm

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by [email protected] » Tue May 22, 2018 2:55 pm

Hi All,

This prompt gives us a number of facts to work with:
1) "A" and "B" run around a circular track starting from the same point simultaneously (and in the same direction)
2) "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round (meaning 4.5 laps complete)
3) "A" is faster than "B" and take 70 seconds to complete 1 lap.

We're asked for the amount of time it takes for B take to complete 1 lap.

Since A is faster than B, we know that they will meet when A has 'lapped' B. Thus, when A has completed 4.5 laps, B has completed just 3.5 laps. We can determine A's total time at 4.5 laps:

(4.5 laps)(70 secs/lap) = 315 seconds

This is the same amount of time that B has been running, so we can determine B's speed:

(3.5 laps)(X secs/lap) = 315 seconds
X = 315/3.5
X = 630/7
X = 90 seconds/lap

Final Answer: A

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Rich

Contact Rich at [email protected]

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue May 22, 2018 3:04 pm

BTGmoderatorLU wrote:"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap?

A. 90 seconds
B. 54.44 seconds
C. 110 seconds
D. 63 seconds
E. 77 seconds

Middle of the 5th round = 4.5 laps. (4 full laps + half of the 5th lap.)
Since A's rate = 70 seconds per lap, the time for A to complete 4.5 laps = (total number of laps)(number of seconds per lap) = (4.5)(70) = 315 seconds.

We can PLUG IN THE ANSWERS, which represent the number of seconds for B to complete 1 lap.
When the correct answer is plugged in, B will complete X.5 laps in 315 seconds to meet A halfway around the track.
Only A works:
(315 seconds)/(90 seconds per lap) = 3.5 laps.

The correct answer is A.

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