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# A car overtakes a goods train, which is 400 m long and running at 36 k

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3367
A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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Updated on: 17 Sep 2018, 17:18
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16
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Difficulty:

85% (hard)

Question Stats:

55% (03:21) correct 45% (02:52) wrong based on 121 sessions

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3 common mistakes you must avoid in Distance questions – Practice question 3

A car overtakes a goods train, which is 400 m long and running at 36 kph, in 8 secs. The same car crosses another goods train, which is running from opposite direction at 54 kph, in 4 secs. How long the faster train will take to cross the slower train?

A. 28 seconds
B. 2 minutes
C. 2 minutes 20 seconds
D. 3 minutes 20 seconds
E. 3 minutes 40 seconds

To read the article: 3 common mistakes you must avoid in Distance questions

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Originally posted by EgmatQuantExpert on 16 May 2018, 06:38.
Last edited by chetan2u on 17 Sep 2018, 17:18, edited 6 times in total.
Formatted question and corrected the OA
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Posts: 8590
A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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17 Sep 2018, 17:16
2
arpitkansal wrote:
chetan2u Bunuel EgmatQuantExpert I am confused with the solution provided.
Correct me if I am wrong.The question nowhere mentions if the trains are moving in the same direction.The language of the question creates an impression that the trains are travelling in the opposite direction.If that is the case then the answer must be (a).

Yes you are correct..

Two cases..
I.. first train
Language is car OVERTAKES the train, so both should be traveling in same direction..
Length of train = 400m
Speed of train =36kmph=36*1000/(3600)meter per sec=10mps
Let speed of car be s, so relative speed =(s-10) as both are traveling in SAME direction
Thus 8*(s-10)=400.....8s-80=400......8s=480........s=60
II. Second train
This train is in OPPOSITE direction
Speed of train =54kph=54000/3600=15mps
Relative speed = 60+15=75mps
Time taken =4s, so distance traveled=4*75=300
This 300 is nothing but length of train.

1) two trains running in OPPOSITE direction OVERTAKING each other.
2) Also time taken to overtake/cross will also include the distance between these two trains. It seems to suggest that they are touching each other.
So poorly worded question in both aspects

But logically they should cross each other and time to overtake after they meet each other would be correct

So total distance to be covered = 400+300=700
Relative speed=10+15=25mps
Time to cross =700/25=28sec

A
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Re: A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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16 May 2018, 06:41

Solution

Given:
• A car overtakes a goods train in 8 seconds
• The length of the goods train = 400 m
• The speed of the goods train = 36 kph = ($$36 * \frac{5}{18}$$) m/s = 10 m/s
• The same car crosses another goods train from opposite direction in 4 seconds
• Speed of the 2nd goods train = 54 kph = ($$54 * \frac{5}{18}$$) m/s = 15 m/s
o Hence, 2nd train is faster than 1st train, as its speed is more than 1st train

To find:
• The time the faster train will take to overtake the slower train

Approach and Working:
As the length of the car is negligible compared to the length of either of the trains, only the lengths of the trains need to be considered while considering the cases

Let us assume the speed of the car as u m/s and length of the 2nd train as l m

• In the 1st case, the car overtakes the 1st goods train in 8 seconds
o Total distance travelled = 400 m [only the length of the train]
o Relative speed = (u – 10) m/s
o Therefore, 8 (u – 10) = 400
Or, u – 10 = 50
Or, u = 60 m/s
• Hence, the speed of the car = 60 m/s

• In the 2nd case, the car crosses the 2nd train from opposite direction in 4 seconds
o Total distance travelled = l m [only the length of the train]
o Relative speed = (60 + 15) m/s = 75 m/s
o Therefore, 75 * 4 = l
Or, l = 300 m
• Hence, the length of the 2nd train = 300 m

• When the 2nd train overtakes the 1st train,
o Total distance travelled = (400 + 300) m = 700 m
o Relative speed = (15 – 10) m/s = 5 m/s
o Therefore, the time taken to overtake = 700/5 secs = 140 secs = 2 minutes 20 seconds

Hence, the correct answer is option C.

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##### General Discussion
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Joined: 30 Jan 2018
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Re: A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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17 Sep 2018, 00:55
3
EgmatQuantExpert wrote:

Solution

Given:
• A car overtakes a goods train in 8 seconds
• The length of the goods train = 400 m
• The speed of the goods train = 36 kph = ($$36 * \frac{5}{18}$$) m/s = 10 m/s
• The same car crosses another goods train from opposite direction in 4 seconds
• Speed of the 2nd goods train = 54 kph = ($$54 * \frac{5}{18}$$) m/s = 15 m/s
o Hence, 2nd train is faster than 1st train, as its speed is more than 1st train

To find:
• The time the faster train will take to overtake the slower train

Approach and Working:
As the length of the car is negligible compared to the length of either of the trains, only the lengths of the trains need to be considered while considering the cases

Let us assume the speed of the car as u m/s and length of the 2nd train as l m

• In the 1st case, the car overtakes the 1st goods train in 8 seconds
o Total distance travelled = 400 m [only the length of the train]
o Relative speed = (u – 10) m/s
o Therefore, 8 (u – 10) = 400
Or, u – 10 = 50
Or, u = 60 m/s
• Hence, the speed of the car = 60 m/s

• In the 2nd case, the car crosses the 2nd train from opposite direction in 4 seconds
o Total distance travelled = l m [only the length of the train]
o Relative speed = (60 + 15) m/s = 75 m/s
o Therefore, 75 * 4 = l
Or, l = 300 m
• Hence, the length of the 2nd train = 300 m

• When the 2nd train overtakes the 1st train,
o Total distance travelled = (400 + 300) m = 700 m
o Relative speed = (15 – 10) m/s = 5 m/s
o Therefore, the time taken to overtake = 700/5 secs = 140 secs = 2 minutes 20 seconds

Hence, the correct answer is option C.

Hi,
First of all thank you for the complete solution but i have a small doubt in last few lines:
Total distance travelled = (400 + 300) m = 700 m
o Relative speed = (15 – 10) m/s = 5 m/s
o Therefore, the time taken to overtake = 700/5 secs = 140 secs = 2 minutes 20 seconds[/list]

Here relative speed should be added as both trains are moving in opposite direction. and in that case answer will be 28sec.
So kindly guide me where I am going wrong in understanding the ques.

Anurag Jain
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Re: A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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17 Sep 2018, 11:10
1
chetan2u Bunuel EgmatQuantExpert I am confused with the solution provided.
Correct me if I am wrong.The question nowhere mentions if the trains are moving in the same direction.The language of the question creates an impression that the trains are travelling in the opposite direction.If that is the case then the answer must be (a).
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Joined: 20 Feb 2015
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A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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18 Sep 2018, 01:02
arpitkansal wrote:
chetan2u Bunuel EgmatQuantExpert I am confused with the solution provided.
Correct me if I am wrong.The question nowhere mentions if the trains are moving in the same direction.The language of the question creates an impression that the trains are travelling in the opposite direction.If that is the case then the answer must be (a).

1. The car overtakes the train ( this tells us that the car and the train are moving in same direction)
Length of the train = distance = 400 m
time taken = 8 seconds
Relative speed= 400/8 = 50 m/s
since the car and the train are moving in the same direction
speed of train = 36 kmph = 36 * 5/18 m/s = 10m/s
speed of car = relative speed + speed of train = 50+10 = 60 m/s

2.The same car crosses the goods train,which is travelling in opposite direction
speed of the train = 54 kmph = 54 * 5/18 = 15 m/s
relative speed = speed of train + speed of car = 60 + 15 = 75 m/s
distance = length of train = 75*4= 300 m

3. Since the trains are travelling in opposite direction
relative speed = speed of train 1 + speed of train 2 = 10 + 15 = 25 m/s
distance = length of both the trains = 400 + 300 = 700
time taken = 700/25 = 28 seconds

A
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Re: A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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04 Jul 2019, 09:26
1
EgmatQuantExpert wrote:

Solution

Given:
• A car overtakes a goods train in 8 seconds
• The length of the goods train = 400 m
• The speed of the goods train = 36 kph = ($$36 * \frac{5}{18}$$) m/s = 10 m/s
• The same car crosses another goods train from opposite direction in 4 seconds
• Speed of the 2nd goods train = 54 kph = ($$54 * \frac{5}{18}$$) m/s = 15 m/s
o Hence, 2nd train is faster than 1st train, as its speed is more than 1st train

To find:
• The time the faster train will take to overtake the slower train

Approach and Working:
As the length of the car is negligible compared to the length of either of the trains, only the lengths of the trains need to be considered while considering the cases

Let us assume the speed of the car as u m/s and length of the 2nd train as l m

• In the 1st case, the car overtakes the 1st goods train in 8 seconds
o Total distance travelled = 400 m [only the length of the train]
o Relative speed = (u – 10) m/s
o Therefore, 8 (u – 10) = 400
Or, u – 10 = 50
Or, u = 60 m/s
• Hence, the speed of the car = 60 m/s

• In the 2nd case, the car crosses the 2nd train from opposite direction in 4 seconds
o Total distance travelled = l m [only the length of the train]
o Relative speed = (60 + 15) m/s = 75 m/s
o Therefore, 75 * 4 = l
Or, l = 300 m
• Hence, the length of the 2nd train = 300 m

• When the 2nd train overtakes the 1st train,
o Total distance travelled = (400 + 300) m = 700 m
o Relative speed = (15 – 10) m/s = 5 m/s
o Therefore, the time taken to overtake = 700/5 secs = 140 secs = 2 minutes 20 seconds

Hence, the correct answer is option C.

Sorry, I still struggle to understand, is the correct answer A or C? As I understood from the question, the trains were moving at the end in the same direction, and thus I chose answer C. However, if to refer to the beginning of the task, the trains were moving in the opposite directions, and the answer in this case would be A. Please could you explain it?
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Re: A car overtakes a goods train, which is 400 m long and running at 36 k  [#permalink]

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02 Apr 2020, 08:05
EgmatQuantExpert wrote:
3 common mistakes you must avoid in Distance questions – Practice question 3

A car overtakes a goods train, which is 400 m long and running at 36 kph, in 8 secs. The same car crosses another goods train, which is running from opposite direction at 54 kph, in 4 secs. How long the faster train will take to cross the slower train?

A. 28 seconds
B. 2 minutes
C. 2 minutes 20 seconds
D. 3 minutes 20 seconds
E. 3 minutes 40 seconds

To read the article: 3 common mistakes you must avoid in Distance questions

First, we can let r = the speed of the car (in kph) and create the equation:

8/3600 x r = 8/3600 x 36 + 400/1000

r/450 = 2/25 + 2/5

Multiplying the equation by 450, we have:

r = 36 + 180

r = 216

Next, we can let n = the length of the faster train (in meters) and create the equation:

4/3600 x 216 + 4/3600 x 54 = n/1000

6/25 + 3/50 = n/1000

Multiplying the equation by 1000, we have:

240 + 60 = n

n = 300

Finally, we can let t = the number of hours it takes the faster train to cross the slower train, and we can create the equation:

36t + 54t = 400/1000 + 300/1000

90t = 7/10

t = 7/900 hr = 28 seconds

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Re: A car overtakes a goods train, which is 400 m long and running at 36 k   [#permalink] 02 Apr 2020, 08:05