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# Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta  [#permalink]

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26 Mar 2019, 23:03
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Difficulty:

15% (low)

Question Stats:

93% (01:43) correct 7% (00:43) wrong based on 14 sessions

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Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs start simultaneously from A and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point D. What is BD?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Attachment:

2007_12B_AMC-6.png [ 6.56 KiB | Viewed 376 times ]

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Joined: 27 Sep 2018
Posts: 37
Re: Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta  [#permalink]

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26 Mar 2019, 23:09
Let BD=x
Therefore,CD=6-BD=6-x

As, speed is same, so the distance will be equal
Thus, 5+x=7+(6-x)
x=4
BD=4

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Re: Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta  [#permalink]

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27 Mar 2019, 01:09
Bunuel wrote:

Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs start simultaneously from A and crawl along the sides of the triangle in opposite directions at the same speed. They meet at point D. What is BD?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Attachment:
2007_12B_AMC-6.png

total distance travelled by two bugs is same
so
7+x=6-x+5
2x=4
x=2
BD= 6-x; 4
IMO D
Re: Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta   [#permalink] 27 Mar 2019, 01:09
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