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Updated on: 17 Sep 2018, 18:18
Originally posted by EgmatQuantExpert on 16 May 2018, 07:38.
Last edited by chetan2u on 17 Sep 2018, 18:18, edited 6 times in total.
Last edited by chetan2u on 17 Sep 2018, 18:18, edited 6 times in total.
Formatted question and corrected the OA
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A
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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?
To read the article: 3 common mistakes you must avoid in Distance questions
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
17 Sep 2018, 18:16
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arpitkansal
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.
Now the question illogically asks
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
16 May 2018, 07:41
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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
• 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
• 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.
Answer: C
