A Train Overtakes Two Persons Who Are Walking In The Same Direction GMAT Problem Solving

Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train (in meters) is

1. 45
2. 50
3. 54
4. 62
5. 72

Correct Answer: (B)
Solutions and Explanation
Approach Solution - 1 :

Let v m/s = train speed
Let L m = train length

For First person (2 km/h)

The first person travels (2*5/18*9) = 5 meters and the train has traveled 9 meters after 9 seconds.
=> 9v = 5 + L, Consider this as equation - (1)

For second person (4 km/h)

The second person moves (4*5/18*10) = 100/9 meters and the train moves 10 meters after 10 seconds.
=> 10v = 100/9 + L , Consider this as equation - (2)

By equations (2) - (1) => v = 55/9 m/s
(1) => 9v - 5 = L = 9(55/9) - 5 = 50 meters

Approach Solution - 2 :

Let t be the train's speed and x be its length.

The train's length is then (t-2)
We are aware that speed = distance/time, so it can also be written as distance = speed * time
In relation to a person moving at a speed of 2 kph, use *9/3600 and (t-4)*10/3600, respectively.

However, the length is the same, so (t-2)
9t - 18 = 10t - 40 = 22 kph *9/3600 = (t-4) *10/3600

Therefore, x = (22-2)*9/3600 = 0.050km = 50m

Approach Solution - 3 :

Consider the length of train as L and speed of train as S.

Speed of person 1 = 2 kmph = 5/9 m/s
Speed of person 2 = 4 kmph = 10.9 m/s

Now, we can write the following equations:

L / [s- (5/9)] = 9, and
L / [s- (10/9)] = 10

By solving the two equations, we can get two variables.

S = 55/9 and L = 50

“A train overtakes two persons who are walking in the same direction ” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

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