Question

a train passes 300 M long platform in 30 second and it crosses a signal on the station in 12 second . find: a)The speed of the train in km/h. b)the length of the. train

Answer 1

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Answer 2

Answer:

(a) Speed of train = 60 km/h

(b) Length of train = 200 m

Explanation:

Let us suppose length of train be x m

Let use suppose speed of train be y m/s

$\text{Formula: Time}=\frac{\text{Distance}}{\text{Speed}}$

Case 1: If train passes platform.

Total distance = (300+x) m

Speed = y m/s

Time = 30 s

$\therefore 30=\frac{300+x}{y} \Rightarrow 30y=300+x$

Case 2: If train passes signal.

Distance =  x m

Speed = y m/s

Time 12 s

$\therefore 12=\frac{x}{y} \Rightarrow 12y=x$

Now, substitute x=12y into equation 30y=300+x and we get

30y=300+12y

30y-12y=300

18y=300

$y=\frac{300}{18}\text{ m/s}$

Now we change speed m/s to km/h

$\text{As we know 1 m/s}=\frac{18}{5}\ km/h$

$\therefore \text{Speed of train }=\frac{300}{18}\times \frac{18}{5} \Rightarrow 60\text{ km/h}$

$\text{Length of train x}=12y\Rightarrow 12\times \frac{300}{18} = 200\ m$