Question

A 200m long train passes a 300m long platform in 5 seconds. If a man is walking at 4m/s along the track and the train is 100m away from him, how much time will it take to reach the man​

Answer 1

A 200 m long train passes a 300 m long platform in 5 s.

Distance travelled by the train = 200 m long train + 300 m long platform = 500 m

Time taken = 5 seconds

Thus speed of the train = distance/time

Speed of the train = 500 m / 5 seconds = 100 m/s

If a man is walking at a speed of 4 m/s along the track and the train is 100 m away from him, how much time will it take to reach the man?

Distance of train from the man = 100 m

Speed = train speed + man's speed

Speed = 100 m/s + 4 m/s = 104 m/s

We know Distance = speed × time

Time = Distance / Speed

Time to be taken by train = 100 m / 104 m per second

Time to ve taken by train = 0.96153seconds rounded to 0.97seconds

The train will take 0.97 seconds or less than a minute to reach the man

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Answer: The train will take 0.88 seconds or less than a second to reach the man

Answer 2

Step-by-step explanation:

$Let\: the\: speed \:of\: train \:to\: be\: s\:. \\</p><p></p><p>Length\: of\: train\: = \:200 \:m \:=\: d1 \\</p><p></p><p>Lenth \:of\: platform \:=\: 300 \:m \:= \:d2 \\</p><p></p><p>Time \:take\: to\:pass\: the \:platform \:= \:5 sec \:= \:t \\</p><p></p><p>Then, \\</p><p> </p><p> \frac{d1 + d2}{s} = t \\ \frac{200 + 300}{s} = 5 \: sec \\ s = \frac{500}{5} \: m \: s {}^{ -1} \\ s= 100 \: m \: {s}^{ - 1} \\</p><p></p><p></p><p></p><p>Now,\\ </p><p>speed \:of\: man\: = \:4 m/sec\\</p><p></p><p> Relative\: speed\: =\: 100 \:m/sec - 4 \:m/sec \:= \:96 \:m/sec\\</p><p> Actual \:distance \:= \: 200+ 100 \:m \:=\: 300\\</p><p></p><p>Then, \\</p><p></p><p>Time\: taken \:to\: pass\: man\: = \frac{\:Actual\: distance} { Relative \:speed} \\</p><p> \: \: \: \: \:= \: \frac{ 300 \:m} {96 m/s} \:=\: 3.13\: seconds \\</p><p>\\ \\ \\</p><p></p><p>$

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