a train running at the rate of 40km an hour meets a person walking along the line in the opposite direction at the rate of 4km an hour and passes him in 45/8 seconds. find the length of the train.had the person been going in the same direction as the train in what time would it have passed him?
Answers
Given :-
- Speed of Train = 40 km/h .
- Speed of person walking in opposite direction = 4km/h .
- Time taken to cross him = (45/8) seconds.
To find :-
- Length of train ?
- Time taken by train to cross the person , if he was moving in same direction ?
Concept used :-
- Distance covered by train when passing a man = Length of Train..
- To change speed from km/h to m/s , multiply it by = (5/18)
- Distance = speed * Time .
- Time = Distance / speed .
- In same direction usual speed = (S2 - S1) .
- in Opposite direction usual speed = (S1 + S1) .
Solution :-
given that,
→ Speed of Train = 40 km/h = 40 * (5/18) = (100/9) m/s.
→ speed of person = 4km/h = 4 * (5/18) = (10/9) m/s.
So,
→ usual speed (in opposite direction) = (100/9) + (10/9) = (110/9) m/s.
and,
→ Time taken by train to cross the person = (45/8) seconds.
Therefore,
→ Distance = Speed * Time.
→ Length of Train = usual speed * Time taken in crossing
→ Length of Train = (110/9) * (45/8) = 68.75 m. (Ans.)
Now,
→ Length of Train = 68.75m.
→ usual speed in same direction = (100/9) - (10/9) = (90/9) = 10 seconds.
Therefore,
→ Time taken to cross the person = D/S = (68.75/10) = 6.875 seconds = (55/8) seconds. (Ans.)
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