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# Two persons A and B run at constant speeds of a miles per hour and b

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Math Expert
Joined: 02 Aug 2009
Posts: 6218
Two persons A and B run at constant speeds of a miles per hour and b [#permalink]

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19 Feb 2016, 21:47
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Difficulty:

85% (hard)

Question Stats:

51% (01:59) correct 49% (01:17) wrong based on 97 sessions

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Two persons A and B run at constant speeds of a miles per hour and b miles per hour respectively. They start running toward each other at the same time from a distance of d miles. What is the speed of A and B?

(1) If A and B ran at speeds of a/2 and 2b respectively, they would take the same amount of time to meet.
(2) If they both ran at 1 mile per hour slower, they would take double the time to meet.

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Two persons A and B run at constant speeds of a miles per hour and b [#permalink]

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21 Feb 2016, 12:54
1
1. d/(a+b)=d/((a/2)+2b) => 2b=a ( not sufficient)
2. d/(a+b-2)=2* d/(a+b) => a+b=4 ( not sufficient)

combining => we can solve for a and b.
=> C
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Re: Two persons A and B run at constant speeds of a miles per hour and b [#permalink]

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23 Feb 2016, 19:00
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Two persons A and B run at constant speeds of a miles per hour and b miles per hour respectively. They start running toward each other at the same time from a distance of d miles. What is the speed of A and B?

(1) If A and B ran at speeds of a/2 and 2b respectively, they would take the same amount of time to meet.
(2) If they both ran at 1 mile per hour slower, they would take double the time to meet.

When you modify the original condition and the question, they become at+bt=d.(t is a time until they meet) That is, there are 4 variables(a,b,t,d) and 1 equation((a+b)t=d), which should match with the number of equations. So you need 3 more equations. For 1) 1 equation, For 2) 1 equation, which is likely to make E the answer.
When 1 & 2), they make (a/2+b)t=d, (a+b-2)2t=d and a+b=2a+2b-4, a/2+b=a+2b -> a=2b -> b=4/3, a=8/3, which is unique and sufficient.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Posts: 6218
Re: Two persons A and B run at constant speeds of a miles per hour and b [#permalink]

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23 Feb 2016, 23:44
2
1
chetan2u wrote:
Two persons A and B run at constant speeds of a miles per hour and b miles per hour respectively. They start running toward each other at the same time from a distance of d miles. What is the speed of A and B?

(1) If A and B ran at speeds of a/2 and 2b respectively, they would take the same amount of time to meet.
(2) If they both ran at 1 mile per hour slower, they would take double the time to meet.

Hi all,

INFO from Q..

1) Both are running towards each other so resultant speed is the addition of both, a+b.

Solution

(1) If A and B ran at speeds of a/2 and 2b respectively, they would take the same amount of time to meet.
Sice time taken is same and the distance is also same, the resultant speed should be same..
so a+b= a/2 + 2b..
a/2 = b.. or a=2b..
we know the ratio of their speed, but not the value of a and b..
Insuff

(2) If they both ran at 1 mile per hour slower, they would take double the time to meet.
so 2d/(a+b)=d/(a+b-2)..
a+b=4..
we just know the sum, but not individual speeds..
Insuff..

Combined--
a=2b and a+b=4...
two variables and two different linear equations..
Suff to find the value of variables
C

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Two persons A and B run at constant speeds of a miles per hour and b [#permalink]

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26 Sep 2017, 04:20
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Re: Two persons A and B run at constant speeds of a miles per hour and b   [#permalink] 26 Sep 2017, 04:20
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