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

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Joe is to swim across the circular pond with center O directly from A  [#permalink]

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11 Sep 2018, 02:01
00:00

Difficulty:

25% (medium)

Question Stats:

83% (02:11) correct 17% (00:09) wrong based on 13 sessions

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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 [ 2.05 KiB | Viewed 371 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 7688
Re: Joe is to swim across the circular pond with center O directly from A  [#permalink]

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11 Sep 2018, 02:18
Bunuel wrote:

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   [#permalink] 11 Sep 2018, 02:18
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