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Joe is to swim across the circular pond with center O directly from A

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Joe is to swim across the circular pond with center O directly from A  [#permalink]

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New post 11 Sep 2018, 01:01
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Joe is to swim across the circular pond with center O directly from A to B, while Sam walks around the pond along the arc ACB. If both Joe and Sam take the same time to make the trip from A to B, and angle AOB is 60° what is the ratio of Joe's swimming speed to Sam's walking speed?


A. \(2:\pi\)

B. \(3:\pi\)

C, \(5:2\pi\)

D. \(8:9\pi\)

E. \(11:12\pi\)

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Re: Joe is to swim across the circular pond with center O directly from A  [#permalink]

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New post 11 Sep 2018, 01:18
Bunuel wrote:
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Joe is to swim across the circular pond with center O directly from A to B, while Sam walks around the pond along the arc ACB. If both Joe and Sam take the same time to make the trip from A to B, and angle AOB is 60° what is the ratio of Joe's swimming speed to Sam's walking speed?


A. \(2:\pi\)

B. \(3:\pi\)

C, \(5:2\pi\)

D. \(8:9\pi\)

E. \(11:12\pi\)

Attachment:
image028.jpg


Since the time is the same, the ratio of speed will depend on distance...

Let us , therefore, measure the distances traveled

1) Arc AB..
Now arc AB extends an angle of 60 with the center..
So the arc will be 2πr*60/360=πr/3

2) line AB..
Central angle is 60. The other two angles will be equal as the sides are equal
So the triangle becomes 60-60-60 equilateral triangle..
Thus AB is r

Ratio r:πr/3 = 3:π

B
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Re: Joe is to swim across the circular pond with center O directly from A &nbs [#permalink] 11 Sep 2018, 01:18
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