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 and 10 seconds respectively. The length of the train is:??
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Answers
Answer:
50m.
Step-by-step explanation:
It is given that the speed of the two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph.
Firstly we will convert the given speed of the two persons from kmph to m/s.
Speed of first person = 2kmph = 2 × 5/18m/s
= 59m/s
Now, Speed of second person
= 4kmph = 4 × 5/18m/s = 9/10m/s
Also, it is given that the train passes them completely in 9 and 10 seconds.
We know that ratio of the distance to the speed is equals to the time.
Let x meters be the length of the train and y m/s be the speed of the train.
Substituting the values in above equation,
we get,
⇒x/(y−5/9) = 9sec
Simplifying the equation, we get
⇒9y−5=x
We will multiply both sides by 10.
Therefore the equation becomes,
⇒90y−50=10x……………… (1)
Time taken by train to cross second person =10sec
⇒distance/speed=10sec
⇒xy−109=10sec
Simplifying the equation, we get
⇒90y−100=9x………………(2)
Now we will subtract equation (2)
from the equation (1) to get the value of x. Therefore, we get
⇒(90y−50)−(90y−100)=10x−9x
Rewriting the above equation, we get
⇒90y−50−90y+100=x
Adding and subtracting the like terms, we get
⇒x=50m
Hence, the length of the train is 50m.