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If t1 hours are required to travel d miles at v1 miles per hour and t2

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If t1 hours are required to travel d miles at v1 miles per hour and t2 [#permalink]

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If t1 hours are required to travel d miles at v1 miles per hour and t2 hours are required to travel the same d miles at v2 miles per hour, is the overall average speed equal to (v1+v2)/2?
1) t1=t2
2) v1=v2

* A solution will be posted in two days.
[Reveal] Spoiler: OA

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Re: If t1 hours are required to travel d miles at v1 miles per hour and t2 [#permalink]

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The Answer is C.I solved i the old traditional way.
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Re: If t1 hours are required to travel d miles at v1 miles per hour and t2 [#permalink]

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MathRevolution wrote:
If t1 hours are required to travel d miles at v1 miles per hour and t2 hours are required to travel the same d miles at v2 miles per hour, is the overall average speed equal to (v1+v2)/2?
1) t1=t2
2) v1=v2

* A solution will be posted in two days.



Ans D
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Re: If t1 hours are required to travel d miles at v1 miles per hour and t2 [#permalink]

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New post 08 May 2016, 20:42
Avg speed= (D1 + d2 + d3 +....... Dn)/(t1+ t2+t3 +..... tn) = ( V1*t1 + V2*t2 + V3*t3 +.......... Sn*tn)/(t1+ t2+t3 +..... tn)

so now for given ques , avg speed= (V1*T1 + V2*T2)/T1+T2.............................. (1)

1st statement , t1=t2 ==> (1) gets reduced to avg speed = (V1+ V2)/2 Sufficient

2nd statement, v1=v2 ==> (1) GETS REDUCED TO avg speed = V1=V2 which is equal to (V1+V2)/2 since both are equal.

Hence Ans D
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Re: If t1 hours are required to travel d miles at v1 miles per hour and t2 [#permalink]

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New post 09 May 2016, 19:43
There are 5 variables (v1, t1, v2, t2, d) and two equations (v1t1=d, v2d2=d) in the original condition. In order to match the number of variables to the number of equations, we need 3 equations. Therefore, there is high chance that E is the correct answer. Using both the condition 1) and the condition 2), we get the condition 1)=the condition 2). The answer is always yes and the conditions are sufficient. Hence, the correct answer is D.

- 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.
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Re: If t1 hours are required to travel d miles at v1 miles per hour and t2 [#permalink]

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New post 26 Dec 2016, 07:59
MathRevolution wrote:
If t1 hours are required to travel d miles at v1 miles per hour and t2 hours are required to travel the same d miles at v2 miles per hour, is the overall average speed equal to (v1+v2)/2?
1) t1=t2
2) v1=v2

* A solution will be posted in two days.


Since it is mentioned that D1=D2, taking any of the T1=T2 or V1=V2 will equate the other dimension. Please correct me if I am wrong.
I think it should be Option D
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If t1 hours are required to travel d miles at v1 miles per hour and t2 [#permalink]

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New post 25 Apr 2017, 11:50
Lastlap2016 wrote:

2nd statement, v1=v2 ==> (1) GETS REDUCED TO avg speed = V1=V2 which is equal to (V1+V2)/2 since both are equal.



I don't understand how v1=v2 can become (v1+v2)/2

Ohhh okay I got it. v1 = (v1+v1)/2. Since v1=v2 then (v1+v2)/2 = (v1+v1)/2.
If t1 hours are required to travel d miles at v1 miles per hour and t2   [#permalink] 25 Apr 2017, 11:50
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