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Homework answers / question archive / Two runners A and B are running round a stadium

Two runners A and B are running round a stadium

Math

Two runners A and B are running round a stadium. A runs faster than B and it takes 3 minutes to A for one lap. A and B started together, and 8 minutes later A caught B for the first time. How long does it take for B to run one lap? A) 6 min B) 8 min C) 4 min 30 s D) 4 min 48 s E) 4 min 20 s

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If 2 people have to meet for the first time on a circular track, the faster person has to complete one full round extra over the slower person. 

 
Let wa and wb be the angular speed of A and B respectively.
 
Given A completes one lap in 3 minutes. Therefore,
 
wa = 2π/3 
 
Therefore, relative speed between A and B = w = wa - wb = 2π/3 - wb
 
They meet after 8 minutes.
 
Therefore, 2π (relative one full round extra) = 8 * (2π/3 - wb)
 
This gives wb = 5π/12
 
Thus, time for one lap for B = 2π / wb = 2π / (5π/12) = 4.8 minutes or 4 min 48 s
 
Correct option is D.
 

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