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Time Speed Distance - Airline Question

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Time Speed Distance - Airline Question  [#permalink]

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New post 16 Aug 2011, 18:04
2
Any idea how to slove this without much caluclation steps... any easy shortcut methodes to get the answer in less than 2 mins ?


Towns X and Y are in countries P and Q respectively. X is 3600 km to the west of Y. An Airline operates non-stop flights between X and Y. Its schedule is tabulated as below. The given time is the local time on the same day.

Departure from Town Y at 4.00PM and Arrival at Town X at 7.30 PM
Departure from Town X at 3.00AM and Arrival at Town Y at 1.30 PM

The planes cruise at the same speed in both directions. However, a steady wind blows from Y to X at 75 KMPH. The effective speed of each plane is affected by this.

Find the time differance between X and Y and the spped at which each plane cruises in KMPH.

A) 2 hrs ; 425 KMPH
B) 2.5 hrs; 525 KMPH
C) 3 hrs; 475 KMPH
D) 4.5 hrs; 550 KMPH
E) 1.5 hrs; 450 KMPH

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Re: Time Speed Distance - Airline Question  [#permalink]

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New post 16 Aug 2011, 20:30
1
cleetus wrote:
Any idea how to slove this without much caluclation steps... any easy shortcut methodes to get the answer in less than 2 mins ?


Towns X and Y are in countries P and Q respectively. X is 3600 km to the west of Y. An Airline operates non-stop flights between X and Y. Its schedule is tabulated as below. The given time is the local time on the same day.

Departure from Town Y at 4.00PM and Arrival at Town X at 7.30 PM
Departure from Town X at 3.00AM and Arrival at Town Y at 1.30 PM

The planes cruise at the same speed in both directions. However, a steady wind blows from Y to X at 75 KMPH. The effective speed of each plane is affected by this.

Find the time differance between X and Y and the spped at which each plane cruises in KMPH.

A) 2 hrs ; 425 KMPH
B) 2.5 hrs; 525 KMPH
C) 3 hrs; 475 KMPH
D) 4.5 hrs; 550 KMPH
E) 1.5 hrs; 450 KMPH


Consider this:
Departure from Town Y at 4.00PM and Arrival at Town X at 7.30 PM
Departure from Town X at 3.00AM and Arrival at Town Y at 1.30 PM

The plane leaves Y at 4:00 PM and is back next day at 1:30 PM i.e. it is out of Y for a total of 21.5 hrs.
The plane reaches X at 7:30 PM and leaves X at 3:00 AM i.e. it rests in X for a total of 7.5 hrs.
This means that it is traveling to and fro for a total of 14 hrs.

Now this question is just like boats and streams. First it travels with the wind so takes less time (downstream) and then it travels against the wind and takes more time (upstream)

Time taken from Y to X = 3600/(s+75)
Time taken from X to Y = 3600/(s - 75)

3600/(s+75) + 3600/(s - 75) = 14
Of course, I am not going to solve this equation. I will try some options. 525 looks good because it is bang in the middle. Also I like the 25 of 525 since it will lead to a better number when we subtract/add 75 to it.

3600/(600) + 3600/(450) = 14
6 + 8 = 14

525 satisfies the equation. Great! Answer is B.

If you want to further verify the time difference, think that from Y to X, the journey takes a total of 6 hrs (downstream). But you leave Y at 4:00 PM and reach X at 7:30 PM. You should reach at 10:00 PM Y time. Hence difference between X and Y time is 2.5 hrs.
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Re: Time Speed Distance - Airline Question  [#permalink]

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New post 19 Aug 2011, 03:40
1
VeritasPrepKarishma wrote:
cleetus wrote:
Any idea how to slove this without much caluclation steps... any easy shortcut methodes to get the answer in less than 2 mins ?


Towns X and Y are in countries P and Q respectively. X is 3600 km to the west of Y. An Airline operates non-stop flights between X and Y. Its schedule is tabulated as below. The given time is the local time on the same day.

Departure from Town Y at 4.00PM and Arrival at Town X at 7.30 PM
Departure from Town X at 3.00AM and Arrival at Town Y at 1.30 PM

The planes cruise at the same speed in both directions. However, a steady wind blows from Y to X at 75 KMPH. The effective speed of each plane is affected by this.

Find the time differance between X and Y and the spped at which each plane cruises in KMPH.

A) 2 hrs ; 425 KMPH
B) 2.5 hrs; 525 KMPH
C) 3 hrs; 475 KMPH
D) 4.5 hrs; 550 KMPH
E) 1.5 hrs; 450 KMPH


Consider this:
Departure from Town Y at 4.00PM and Arrival at Town X at 7.30 PM
Departure from Town X at 3.00AM and Arrival at Town Y at 1.30 PM

The plane leaves Y at 4:00 PM and is back next day at 1:30 PM i.e. it is out of Y for a total of 21.5 hrs.
The plane reaches X at 7:30 PM and leaves X at 3:00 AM i.e. it rests in X for a total of 7.5 hrs.
This means that it is traveling to and fro for a total of 14 hrs.

Now this question is just like boats and streams. First it travels with the wind so takes less time (downstream) and then it travels against the wind and takes more time (upstream)

Time taken from Y to X = 3600/(s+75)
Time taken from X to Y = 3600/(s - 75)

3600/(s+75) + 3600/(s - 75) = 14
Of course, I am not going to solve this equation. I will try some options. 525 looks good because it is bang in the middle. Also I like the 25 of 525 since it will lead to a better number when we subtract/add 75 to it.

3600/(600) + 3600/(450) = 14
6 + 8 = 14

525 satisfies the equation. Great! Answer is B.

If you want to further verify the time difference, think that from Y to X, the journey takes a total of 6 hrs (downstream). But you leave Y at 4:00 PM and reach X at 7:30 PM. You should reach at 10:00 PM Y time. Hence difference between X and Y time is 2.5 hrs.


Thanks for that detailed explanation Karishma..... Great help. +1 to u. Ur exp always helps me in catching the concept.
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Re: Time Speed Distance - Airline Question  [#permalink]

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New post 19 Aug 2011, 05:36
VeritasPrepKarishma wrote:
cleetus wrote:
Any idea how to slove this without much caluclation steps... any easy shortcut methodes to get the answer in less than 2 mins ?


3600/(s+75) + 3600/(s - 75) = 14
Of course, I am not going to solve this equation. I will try some options. 525 looks good because it is bang in the middle. Also I like the 25 of 525 since it will lead to a better number when we subtract/add 75 to it.

3600/(600) + 3600/(450) = 14
6 + 8 = 14

525 satisfies the equation. Great! Answer is B.

If you want to further verify the time difference, think that from Y to X, the journey takes a total of 6 hrs (downstream). But you leave Y at 4:00 PM and reach X at 7:30 PM. You should reach at 10:00 PM Y time. Hence difference between X and Y time is 2.5 hrs.


What if the question asks u to find only the time difference between two countries and no information about the speed, i.e, 525 km per hour is not mentioned in the question. Do u need to do the lengthy algebraic calculation for 3600/(s+75) + 3600/(s - 75) = 14 . Or is there any easy Go.
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Re: Time Speed Distance - Airline Question  [#permalink]

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New post 23 Aug 2011, 20:09
cleetus wrote:

What if the question asks u to find only the time difference between two countries and no information about the speed, i.e, 525 km per hour is not mentioned in the question. Do u need to do the lengthy algebraic calculation for 3600/(s+75) + 3600/(s - 75) = 14 . Or is there any easy Go.


You will almost never need to solve this equation and in GMAT, I can say will reasonable certainty that you will 'never ever' need to solve it the long way. In such questions time taken is generally an integral value.

Even if 525 is not there in the options, look at the big picture

3600/(s+75) + 3600/(s - 75) = 14

The two terms on the left hand side add up to give 14 hrs. Obviously the first term is smaller and the second term is greater. I can split 14 into 6 hrs and 8 hrs OR 5 and 9 OR 4 and 10 etc

Now, wind will have some effect on the time taken but it may not be very dramatic. So, I will first try 6 and 8.

I say, what if 3600/(s + 75) is 6 hrs? i.e. what if s+75 is 600? i.e. what if s is 525? I plug s = 525 in 3600/(s - 75) and see that I do get 8. Then s must be 525!
Had 6 and 8 not worked, I would have tried 5 and 9.

Another thing:
Say the equation is: 770/(s + 20) + 770/(s - 20) = 18
I can split 18 into 8 and 10 OR 7 and 11 etc.
I will not try 8 and 10 here because 770 is not divisible by 8 so no way can I get an integer value for the time i.e. I cannot get 8 hrs.
I will jump to 7 and 11 first.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

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Re: Time Speed Distance - Airline Question  [#permalink]

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Re: Time Speed Distance - Airline Question   [#permalink] 31 Jan 2019, 06:27
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