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A and B start running simultaneously. A r

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A and B start running simultaneously. A r  [#permalink]

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New post 08 Feb 2019, 23:22
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A
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D
E

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A and B start running simultaneously. A runs from point P to point Q and B from point Q to point P. AA's speed is 6/5 of B's speed. After crossing B, if A takes 5/2 hr to reach Q, how much time does BB take to reach PP after crossing A?
A.3 hr 6 min
B.3 hr 16 min
C.3 hr 26 min
D.3 hr 36 min
E 3 hr
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New post 09 Feb 2019, 00:40
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Let's assume arbitrary values for speeds of A and B: B - 50 kmph and A - 60 kmph

If the total distance from P to Q is x km, the point at which A and B make contact is 5/2 * 60 or 150 kms from Q.
The total distance of B from point P is x - 150. The time taken for A and B to reach the point is the same.

Equating the times we get \(\frac{150 - x}{60} = \frac{150}{50}\) -> \(x = 330\)

The total distance that B travels towards P after the point of contact is 180km.

Therefore, B will take \(\frac{180}{50} * 60 = 216\)minutes or 3 hour, 36 minutes(Option C) to reach P after crossing A.
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Re: A and B start running simultaneously. A r  [#permalink]

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New post 26 Feb 2019, 10:44
pushpitkc wrote:
Attachment:
Diagram.png


Let's assume arbitrary values for speeds of A and B: B - 50 kmph and A - 60 kmph

If the total distance from P to Q is x km, the point at which A and B make contact is 5/2 * 60 or 150 kms from Q.
The total distance of B from point P is x - 150. The time taken for A and B to reach the point is the same.

Equating the times we get \(\frac{150 - x}{60} = \frac{150}{50}\) -> \(x = 330\)

The total distance that B travels towards P after the point of contact is 180km.

Therefore, B will take \(\frac{180}{50} * 60 = 216\)minutes or 3 hour, 36 minutes(Option C) to reach P after crossing A.


Maybe I am missing something, but can you please tell me why the time taken for A and B to reach the point is the same? For both A and B we assumed different speeds.
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A and B start running simultaneously. A r  [#permalink]

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New post 26 Feb 2019, 10:55
arorni wrote:
pushpitkc wrote:
Attachment:
Diagram.png


Let's assume arbitrary values for speeds of A and B: B - 50 kmph and A - 60 kmph

If the total distance from P to Q is x km, the point at which A and B make contact is 5/2 * 60 or 150 kms from Q.
The total distance of B from point P is x - 150. The time taken for A and B to reach the point is the same.

Equating the times we get \(\frac{150 - x}{60} = \frac{150}{50}\) -> \(x = 330\)

The total distance that B travels towards P after the point of contact is 180km.

Therefore, B will take \(\frac{180}{50} * 60 = 216\)minutes or 3 hour, 36 minutes(Option C) to reach P after crossing A.


Maybe I am missing something, but can you please tell me why the time taken for A and B to reach the point is the same? For both A and B we assumed different speeds.


Hey arorni

Since both of them start simultaneously, the point at which they meet has to be the same.

Hope that helps
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Re: A and B start running simultaneously. A r  [#permalink]

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New post 26 Feb 2019, 13:01
Yup. you are right.

Thanks,
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Re: A and B start running simultaneously. A r   [#permalink] 26 Feb 2019, 13:01
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