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# M10-08

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:41
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85% (hard)

Question Stats:

47% (01:53) correct 53% (02:23) wrong based on 89 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) $$x = 20$$
[Reveal] Spoiler: OA

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16 Sep 2014, 00:41
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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.

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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;

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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;

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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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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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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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Joined: 03 May 2014
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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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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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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Intern
Joined: 09 Sep 2015
Posts: 26

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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
Amaresh
Re: M10-08   [#permalink] 17 Mar 2018, 08:18
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# M10-08

Moderators: chetan2u, Bunuel

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