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M10-08

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M10-08  [#permalink]

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New post 16 Sep 2014, 00:41
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49% (02:13) correct 51% (02:24) wrong based on 94 sessions

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To arrive at its destination on time the bus should have maintained a speed of \(v\) kilometers per hour throughout the journey. Instead, after going the first third of the distance at \(v\) kilometers per hour, the bus increased its speed and went the rest of the distance at \(1.2v\) kilometers per hour. As a result, the bus arrived at its destination \(x\) minutes earlier than planned. What was the actual duration of the trip?


(1) \(v = 60\)

(2) \(x = 20\)

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Re M10-08  [#permalink]

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New post 16 Sep 2014, 00:41
Official Solution:


A bus covered \(\frac{1}{3}\) of the distance at \(v\) kilometers per hour and the remaining \(\frac{2}{3}\) of the distance at \(1.2v\) kilometers per hour.

Say the actual duration of the trip is \(t\) and the distance is \(d\);

Then \(t=\frac{(\frac{d}{3})}{v}+\frac{(\frac{d2}{3})}{1.2v}\), which simplifies to \(t=\frac{d}{v}*(\frac{1}{3}+\frac{2}{3.6})\), and finally to \(t=\frac{d}{v}*\frac{8}{9}\)

Also we know that if the speed throughout the journey had been \(v\) kilometers per hour the bus would need \(\frac{x}{60}\) hours more time to cover the same distance: \(t+\frac{x}{60}=\frac{d}{v}\);

Substitute \(\frac{d}{v}\) in the first equation: \(t=(t+\frac{x}{60})*\frac{8}{9}\). So, to get \(t\) we need to know the value of \(x\).

(1) \(v = 60\). Not sufficient.

(2) \(x = 20\). Sufficient.


Answer: B
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Re: M10-08  [#permalink]

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New post 01 Mar 2017, 12:23
I did not understand this part:

Also we know that if the speed throughout the journey had been v kilometers per hour the bus would need x/60 hours more time to cover the same distance: t+x/60=d/v;

Please explain
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Re: M10-08  [#permalink]

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New post 04 Mar 2017, 03:18
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banerjeeankush99 wrote:
I did not understand this part:

Also we know that if the speed throughout the journey had been v kilometers per hour the bus would need x/60 hours more time to cover the same distance: t+x/60=d/v;

Please explain


Usual time to cover d kilometres at v kilometers per hour is (time) = (distance)/(rate) = d/v. We know that as a result of an acceleration, the bus arrived at its destination x minutes (which is x/60 hours) earlier than planned. Therefore \(t+\frac{x}{60}=\frac{d}{v}\).

Does this make sense?
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Re: M10-08  [#permalink]

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New post 10 Dec 2017, 08:29
Hi Bunuel, I believe statement-1 is sufficient.

Given in question stem, Bus should have maintained a speed of v kilometer/hr. After going the first third of the distance at v kilometers per hour.

Statement-1, V = 60.
Therefore total distance 180 km. ( as it is given first third of the distance at v km per hour).
Total planned duration = 3 hours
Actual duration = 2.6 hours ( first hour 60 km/hr, remaining 2 hr at 72 km/hr)

What am I missing?
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Re: M10-08  [#permalink]

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New post 10 Dec 2017, 08:40
ManSab wrote:
Hi Bunuel, I believe statement-1 is sufficient.

Given in question stem, Bus should have maintained a speed of v kilometer/hr. After going the first third of the distance at v kilometers per hour.

Statement-1, V = 60.
Therefore total distance 180 km. ( as it is given first third of the distance at v km per hour).
Total planned duration = 3 hours
Actual duration = 2.6 hours ( first hour 60 km/hr, remaining 2 hr at 72 km/hr)

What am I missing?



You are wrongly interpreting the Q..
it is \(\frac{1}{3}\) of distance and not time..

so if distance was 60km.. duration would have been 60/60=1
but actually he traveled distance of 20 at 60km/h and next 40 km at 1.2*60=72km/h

distance is 180.. duration 3 hrs and so on
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: M10-08  [#permalink]

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New post 10 Dec 2017, 08:54
Thanks chetan2u for taking time to respond.
I am still struggling.Let me give it one more try.

Question stem says Bus should have maintained speed of v km/hr and then for 1/3rd of distance it maintained V km/hr and remaining at 1.2v.
Now let's plug in statement-1 V=60.
Bus should have maintained speed of 60 km/hr and then going 1/3rd of distance at 60 km/hr and remaining at 72 km/hr.
Now, I can safely conclude that total distance is 180 km. Total planned duration was 3 hours.
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Re: M10-08  [#permalink]

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New post 10 Dec 2017, 09:02
ManSab wrote:
Thanks chetan2u for taking time to respond.
I am still struggling.Let me give it one more try.

Question stem says Bus should have maintained speed of v km/hr and then for 1/3rd of distance it maintained V km/hr and remaining at 1.2v.
Now let's plug in statement-1 V=60.
Bus should have maintained speed of 60 km/hr and then going 1/3rd of distance at 60 km/hr and remaining at 72 km/hr.
Now, I can safely conclude that total distance is 180 km. Total planned duration was 3 hours.




Hi..

In that case you don't require statement I at all.
You already know 1/3 is 1 HR... 1/3 at v and 1/3 at 1.2v
So irrespective of v, as per your method, Ans is 3
But that's not correct.

1/3 of distance does not mean 1/3 of time. You are mixing the two here.
It is given 1/3 of distance at v and then at 1.2v.
Your answer would depend on distance or the difference in time as shown above
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Re: M10-08  [#permalink]

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New post 17 Mar 2018, 08:18
Hi,

I have a query here.
Can we assume the distance ? If we can then let us assume 60km So 1/3rd will be 20km at "v" kmph and rest 60km at "1.2v" kmph.
If we follow this approach then we need the value of "v" . From this we can find total time (t1+t2) .
Is this correct ? Can we assign values to the distance if it is not given in question stem ?

Any help is appreciated

Thanks
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Re: M10-08  [#permalink]

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New post 09 May 2018, 11:46
Not sure if the logic that I used makes sense, but we're give some information about Speed v in the question stem, and
Distance = Speed * Time, don't we need information about one or the other of time or distance to solve? That logic worked here, (statement 2 is correct because we're given something about one of the other two variables not mentioned in the stem) but I'm not sure if that was just luck or not.
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Re: M10-08 &nbs [#permalink] 09 May 2018, 11:46
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