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505-555 (Easy)|   Geometry|      
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Bunuel
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Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta 26 Mar 2019, 23:03
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88% (01:44) correct 12% (01:26) wrong based on 57 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

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itsanujsingh
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Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta 26 Mar 2019, 23:09
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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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Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta 27 Mar 2019, 01:09
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Bunuel

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

Show Spoiler
Attachment:
2007_12B_AMC-6.png
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total distance travelled by two bugs is same
so
7+x=6-x+5
2x=4
x=2
BD= 6-x; 4
IMO D
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Triangle ABC has side lengths AB = 5, BC = 6, and AC = 7. Two bugs sta 13 Oct 2020, 06:21
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itsanujsingh
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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itsanujsingh, Archit3110,

How did both of you arrive at the conclusion that the distance travelled by both the bugs is the same?

If speed is same will the distance be equal? Not necessarily.It depends on travelling duration.
Let speed be 5 m/h and time be 2h then distance travelled = 5*2 =10 Miles
Let speed be 5 m/h and time be 3h then distance travelled = 5*3 =15 Miles

As shown above, speed being same is no guarantee that distance travelled will be equal

The problem can be solved only if we assume that they took same time to reach point D.
Let T be the time each took to reach point D , since time is same we can equate the time taken by each bug.

\(\frac{7+x}{s}=\frac{5+6-x}{s}\)

Where S is the speed and x is distance CD.
Solving the above we will get \(x= 4 \)

Hope this makes sense.
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