On the bridge 400 meters long there is a train for 30 seconds, and past a man – 10 seconds.
| April 27, 2021 | education
On the bridge 400 meters long there is a train for 30 seconds, and past a man – 10 seconds. Find the length and speed of the train.
Lm = 400 m.
tm = 30 s.
tch = 10 s.
Lп -?
Vп -?
We express the speed of the train Vp by the formula: Vp = Lp / tch.
The time of movement of the train on the bridge is expressed by the formula: tm = (Lm + Lp) / Vp.
Vp = (Lm + Lp) / tm.
Lp / tch = (Lm + Lp) / tm.
Lm * tch + Lp * tch = Lp * tm.
Lm * tch = Lp * (tm – tch).
The length of the train Lp will be determined by the formula: Lp = Lm * tch / (tm – tch).
Lp = 400 m * 10 s / (30 s – 10 s = 200 m.
Vp = 200 m / 10 s = 20 m / s.
Answer: a train with a length of Lp = 200 m moves along the bridge with a speed of Vp = 20 m / s.
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