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To arrive at its destination on time, a bus should have maintained

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Knesl
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To arrive at its destination on time, a bus should have maintained [#permalink] New post   Updated on: 14 Aug 2023, 09:37
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To arrive at its destination on time, a bus should have maintained a speed of \(v\) kilometers per hour throughout the journey. However, after traveling the first third of the distance at \(v\) kilometers per hour, the bus increased its speed and covered 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) \(x = 20\)


M10-08

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B

Originally posted by Knesl on 22 Nov 2010, 10:40.
Last edited by Bunuel on 14 Aug 2023, 09:37, edited 2 times in total.
Edited the question.
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   22 Nov 2010, 18:59
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Knesl wrote:
hi,

can somebody help me with following question? I would need the explanation.
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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. \(X = 20\)

(C) 2008 GMAT Club - m10#8

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Thanks!!!


A trick used by GMAT is that they give you similar looking data in the two statements (e.g. in this question, value of one variable given in each statement) and you feel that either each alone will be sufficient or both together. But analyzing the data shows that only one statement is sufficient, the other is not.

The bus covers 1/3 of distance at speed V. The rest 2/3 at speed 1.2V

___________________________
.....V........ ----------1.2V----------

Usual time for the journey is, lets say, T hours, but it arrived in T - X/60 hours. (X is in minutes so you have to change it to hours)

Now, out of the usual T hours, in first 1/3rd of the journey, the bus takes T/3 hours. In rest 2/3rd of the journey, the bus usually takes 2T/3 hours.
During this particular journey, the bus took T/3 hours for the first 1/3rd of the trip (since it traveled at speed V) but for the rest 2/3rd of the trip, it took less time since it traveled at greater speed of 6V/5 (Convert decimals to fractions)
If speed becomes 6/5 of original, time taken will become 5/6 of original.
So time taken to travel 2/3rd of the trip is 5/6 * 2T/3 = 5T/9 hours

In this trip, the total time taken = T/3 + 5T/9 = 8T/9
So the X/60 hours that are saved are equal to T - 8T/9 = T/9

X/60 = T/9

Statement 1: Just V doesn't help. You need D too to get the value of T. Not sufficient.

Statement 2: Knowing just X is sufficient to get T as seen above. Sufficient.

Answer (B).
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   21 Jan 2011, 10:26
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good question.
there's a difference of X "mins" by varying speed in the last \(\frac{2}{3}\) distance, so from the given info, we can write.

\(\frac{2D}{3V} - \frac{2D}{3*1.2V} = \frac{X}{60}\)

\(\frac{2D}{3V}(1 - \frac{1}{1.2}) = \frac{X}{60}\)

\(\frac{D}{V}= \frac{3X}{20}\)

Note: \(\frac{D}{V} =\) "actual duration" of the trip (and this is what we want to find).

1) we still don't know the value of X, so we can't calculate \(\frac{D}{V}\)

2) \(\frac{D}{V}= \frac{3*20}{20}\)

actual time = 3 hrs .... B is SUFFICIENT
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   22 Nov 2010, 10:50
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D/v - D/1.2v = X


1.Given V=60 A is not sufficient since we have 2 variables to be resolved in the above equation
2.Given X=20 B is sufficient as-
D/v-D/1.2v = 20
Solving above equation, V is cancelled out leaving value for D which is sufficient.


Answer:- B
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   01 Nov 2011, 23:34
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beckee529 wrote:
To arrive at its destination on time the bus should have maintained a speed of V kmh throughout the journey. Instead, after going the first third of the distance at V kmh, the bus increased its speed and went the rest of the distance at (1.2)*V kmh. 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


Here is my take.
Let the actual duration of the trip be t.
Distance is same in both the cases.
So, V*t = Increased Average Speed*(t - X/60)

What is the Increased Average Speed?
Average Speed = Total Distance/Total Time = \(\frac{1}{[\frac{\frac{1}{3}}{V} + \frac{\frac{2}{3}}{1.2V}]}\)
We will get this increased average speed in terms of V.

When we put it in the equation above, V will get canceled leaving us with t in terms of X. So to get t, we only need X.
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   25 Jan 2014, 10:48
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To arrive at its destination on time, a bus should have maintained a speed of \(v\) kilometers per hour throughout the journey. However, after traveling the first third of the distance at \(v\) kilometers per hour, the bus increased its speed and covered 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?

The 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.

Let the actual duration of the trip be \(t\) hours and the total distance be \(d\) kilometers. Then we have:

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

We also know that if the speed throughout the journey had been \(v\) kilometers per hour, the bus would have needed \(\frac{x}{60}\) hours more time to cover the same distance: \(t + \frac{x}{60} = \frac{d}{v}\).

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

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

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


Answer: B
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   04 Aug 2015, 06:53
VeritasPrepKarishma wrote:
Knesl wrote:
hi,

can somebody help me with following question? I would need the explanation.
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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. \(X = 20\)

(C) 2008 GMAT Club - m10#8

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Thanks!!!


A trick used by GMAT is that they give you similar looking data in the two statements (e.g. in this question, value of one variable given in each statement) and you feel that either each alone will be sufficient or both together. But analyzing the data shows that only one statement is sufficient, the other is not.

The bus covers 1/3 of distance at speed V. The rest 2/3 at speed 1.2V

___________________________
.....V........ ----------1.2V----------

Usual time for the journey is, lets say, T hours, but it arrived in T - X/60 hours. (X is in minutes so you have to change it to hours)

Now, out of the usual T hours, in first 1/3rd of the journey, the bus takes T/3 hours. In rest 2/3rd of the journey, the bus usually takes 2T/3 hours.
During this particular journey, the bus took T/3 hours for the first 1/3rd of the trip (since it traveled at speed V) but for the rest 2/3rd of the trip, it took less time since it traveled at greater speed of 6V/5 (Convert decimals to fractions)
If speed becomes 6/5 of original, time taken will become 5/6 of original.
So time taken to travel 2/3rd of the trip is 5/6 * 2T/3 = 5T/9 hours

In this trip, the total time taken = T/3 + 5T/9 = 8T/9
So the X/60 hours that are saved are equal to T - 8T/9 = T/9

X/60 = T/9

Statement 1: Just V doesn't help. You need D too to get the value of T. Not sufficient.

Statement 2: Knowing just X is sufficient to get T as seen above. Sufficient.

Answer (B).


I almost got to the last step but could not arrive at the answer...can someone help..Pls...

my steps:

let distance = d
new avg speed = \(\frac{total dist}{total time}\) = \(\frac{3.4vd}{t-x}\)

equating the 2 distances

\(v*t = 3.4 V*d\)

t=3.4d

I got stuck here...
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   04 Aug 2015, 09:23
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robinpallickal wrote:

I almost got to the last step but could not arrive at the answer...can someone help..Pls...

my steps:

let distance = d
new avg speed = \(\frac{total dist}{total time}\) = \(\frac{3.4vd}{t-x}\)

equating the 2 distances

\(v*t = 3.4 V*d\)

t=3.4d

I got stuck here...


I do not understand the expression 3.4vd/(t - x) and also how you arrived at it. Also, x is in minutes while speed is in miles per hour so t should be in hours. Hence t - x doesn't mean anything. It must be t - x/60.
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   25 Aug 2015, 10:20
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I solved the question as below :

Distance = D + D + D ---------------------------- (Total distance = 3D)
Speed = V , 1.2V , 1.2V -----------------------------(Speed for each part)
Time = T + (5/6)T + (5/6)T -----------------------------(Time taken for each part)
Reduced Time = (1/6)T + (1/6)T

Using option B we know that the reduced time is 20 = (1/6T)*2
Hence B.
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   25 Aug 2015, 21:23
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NickHalden wrote:
I solved the question as below :

Distance = D + D + D ---------------------------- (Total distance = 3D)
Speed = V , 1.2V , 1.2V -----------------------------(Speed for each part)
Time = T + (5/6)T + (5/6)T -----------------------------(Time taken for each part)
Reduced Time = (1/6)T + (1/6)T

Using option B we know that the reduced time is 20 = (1/6T)*2
Hence B.


Great use of Speed-Time ratios!

Just note that it should be
20/60 = (1/6)2T

because 20 is in mins but everything else is in hours.
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   29 Nov 2015, 11:12
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Knesl wrote:
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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) \(X = 20\)

(C) 2008 GMAT Club - m10#8

Thanks!!!


--------------------------------------------------------------------------------------
Always remember, in case of inverse relationship such as this an increase of 1/x times of V (velocity) should be accompanied by a decrease of 1/(x+1) in T (time), so as to keep the overall value = V*T = distance constant.

There V -> 1.2 V hence V increases by 20% or 1/5 times, hence the time should be decrease by 1/6th time.

Now, it's already given that the 1/6th of T is X ( in other words the change in duration is already given where the T is the actual duration time)

thus (1/6) * T =X ; T=6X.

Hence just knowing X will give you the solution. So, here B itself is enough, but A is not enough. Answer - B.
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   27 Jan 2019, 23:02
Knesl wrote:
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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) \(X = 20\)

(C) 2008 GMAT Club - m10#8

Thanks!!!


@vertiaskarishma Bunuel chetan2u

With alone A is also correct
Since 1/3 of the distance is 60 km and it took one our to cover it
Since bus should have maintained same speed i.e 60 km/h so it will take additional 2 hr to cover the distance so the actual trip time will be 3 hrs
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   27 Jan 2019, 23:18
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teaserbae wrote:
Knesl wrote:
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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) \(X = 20\)

(C) 2008 GMAT Club - m10#8

Thanks!!!


@vertiaskarishma Bunuel chetan2u

With alone A is also correct
Since 1/3 of the distance is 60 km and it took one our to cover it
Since bus should have maintained same speed i.e 60 km/h so it will take additional 2 hr to cover the distance so the actual trip time will be 3 hrs


Hey teaserbae!

You have assumed a total distance of 180 km (speed of 60 kmph for 1 hr covering a distance of 60 km).
All we know is that 1/3rd the distance is at a speed of 60 kmph. The total distance could very well be 300 km such that 100 km was covered at 60 kmph in a total time of 100/60 = 5/3 hrs
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   11 Mar 2020, 08:12
Quote:
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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) \(X = 20\)

(C) 2008 GMAT Club - m10#8

Thanks!!!


HI GMATGuruNY, MentorTutoring ,GMATBusters GMATinsight

Is there any other way to solve this problem. It took me more than 2mins :-(
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   Updated on: 11 Mar 2020, 21:43
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NandishSS wrote:
Quote:
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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) \(X = 20\)

(C) 2008 GMAT Club - m10#8

Thanks!!!


HI GMATinsight

Is there any other way to solve this problem. It took me more than 2mins :-(


Let, Total Distance = 3D

Time taken to travel first one third distance = D/V
Time taken to travel remaining distance = 2D/1.2V

Now, (D/V) + (2D/1.2V) = (3D/V) - (X/60)

I.e. (D/V)[1+ (2/1.2) - 3) = - (X/60)

Question: Actual Duration = 3D/V = ?

To answer this question, we only need the value of X

Statement 1:\(V = 60\)

NOT SUFFICIENT

Statement 2:\(X = 20\)

SUFFICIENT

Answer: Option B

NandishSS

Originally posted by GMATinsight on 11 Mar 2020, 08:23.
Last edited by GMATinsight on 11 Mar 2020, 21:43, edited 1 time in total.
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   11 Mar 2020, 08:57
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Whenever the speed is multiplied by factor k, the time taken is divided by k.


For example, if speed is doubled, the time is halved.


As per the question,
after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh

let time for first 1/3 distance = t
then the time taken for next 2/3 distance at the same speed =2/3t
so total time = t+2/3t = 5/3t

when speed is made 1.2v, time is divided by 1.2 , hence, new time = (2/3t)/1.2

the difference in time is 2/3t - (2/3t)/1.2 = x
now as per St 2, we know x, hence t can be calculated.

this question can be done in 15-20 sec.
no need to form the equations, we just know that difference in time is a function of original time, hence it can be calculated.


NandishSS wrote:
Quote:
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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) \(X = 20\)

(C) 2008 GMAT Club - m10#8

Thanks!!!


HI GMATGuruNY, MentorTutoring ,GMATBusters GMATinsight

Is there any other way to solve this problem. It took me more than 2mins :-(
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   11 Mar 2020, 12:07
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Knesl wrote:
To arrive at its destination on time, a bus should have maintained a speed of \(V\) kmh throughout its journey. Instead, after going the first third of the distance at \(V\) kmh, the bus increased its speed and went the rest of the distance at \((1.2)*V\) kmh. If, 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) \(X = 20\)

(C) 2008 GMAT Club - m10#8

Thanks!!!



Let T = the normal time for the last 2/3 of the distance, implying that the time for the first 1/3 of the distance \(= \frac{1}{2}T\).
Since the time for the trip is decreased by X minutes, we get:
Time \(= T + 1/2T - X\)

Rate and time have a RECIPROCAL RELATIONSHIP.
Since the rate for the last 2/3 of the distance \(= 1.2V = \frac{6}{5}V\), the time for the last 2/3 of the distance = \(\frac{5}{6}T\).
The expression in blue implies that the time for the last 2/3 of the distance DECREASES BY \(\frac{1}{6}\).
Thus, the X minutes saved at the higher speed is equal to \(\frac{1}{6}T\):
\(X = \frac{1}{6}T\)
\(T = 6X\)

Substituting \(T=6X\) into the green equation above, we get:
Time \(= 6X + \frac{1}{2}(6X) - X = 8X\)

Question stem, rephrased:
What is the value of X?

Statement 1: V=60
No information about X.
INSUFFICIENT

Statement 2: X=20
SUFFICIENT

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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   11 Mar 2023, 21:54
dimitri92 wrote:

good question.
there's a difference of X "mins" by varying speed in the last \(\frac{2}{3}\) distance, so from the given info, we can write.

\(\frac{2D}{3V} - \frac{2D}{3*1.2V} = \frac{X}{60}\)

\(\frac{2D}{3V}(1 - \frac{1}{1.2}) = \frac{X}{60}\)

\(\frac{D}{V}= \frac{3X}{20}\)

Note: \(\frac{D}{V} =\) "actual duration" of the trip (and this is what we want to find).

1) we still don't know the value of X, so we can't calculate \(\frac{D}{V}\)

2) \(\frac{D}{V}= \frac{3*20}{20}\)

actual time = 3 hrs .... B is SUFFICIENT



Hey dimitri92

why is my answer different, let me know if there is any misunderstanding

T1 = D/(3*V) ----------> Time Taken to cover D distance
T2 = 2D/(3*1.2*V) ----> Time Taken to cover 2D/3 distance

Now Statement says Total time taken for this trip is 10 minutes less than time at which trip actually completes

Therefore

(D/V) - (D/(3*V) + 2D/(3*1.2*V)) = 10/60

(D/V) - (3.2 D/3.6 V) = 10/60

D/V - 8D/9V = 10/60

D/9V = 10/60

D/V = 3/2 ==> D/V = 1.5 hrs
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Re: To arrive at its destination on time, a bus should have maintained [#permalink] New post   14 Aug 2023, 09:34
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Re: To arrive at its destination on time, a bus should have maintained [#permalink]
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