A and B walk around a circular track they start at 8 am from the same point in the opposite diretions A and B walk at a speed of 2 rounds per hour and 3 round p

Question

A and B walk around a circular track they start at 8 am from the same point in the opposite diretions A and B walk at a speed of 2 rounds per hour and 3 round per hour respectively how many times shall they cross each other before 9.30 am

 

 

i dont understand concept of this problem please explain me the equation how to form

Answer 1

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Answer 2

Think of this as a work problem.

A does 1 round per 30 minutes

B does 1 round per 20 minutes

How many minutes would it take making a round together?

x/30 + x/20 = 1

2x + 3x = 60

5x = 60

x = 12

 

The meet every 12 minutes. 

How many 12 minute periods are there from 8:00 am to 9:30 am?

Answer 3

Amey,

 

It looks like by "rounds per hour" you mean "number of times around the track per hour." 

 

A walks around twice in one hour and B walks around 3 times per hour. Their rates of walking are respectively 1/2 and 1/3 circumferences per hour. One may consider these as their speeds around the track.

 

You were given that the track was circular. The problem is then, once they start at the same point and walk in opposite directions, how many times will they meet in 90 minutes, or 3/2 hour?

 

One way to do this is to locate their positions around the track by using xy-coordinates for points on the circle.

 

After t hours, A will have walked t/2 circumferences. Since one circumference corresponds to 2π distance units (assuming the radius of the circle is one), A will have walked through an angle of πt radians and will be located at the point (cos πt , sin πt). By similar reasoning, B will be located at the point (cos 2πt/3 , −sin 2πt/3). The minus sign is there because the walking is in the opposite direction. If you do not know what cos and sin are, please let me know before I send you any more help.

 

Once you have described their positions in terms of t, you can find when they meet each other by setting the two points equal to each other (x and y-coordinates), then solving for t, with 0 ≤ t ≤ 3/2.

 

After I receive your answer to the last question (about cos and sin), I can help you finish the problem.

 

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