Question

A train passes 300m long platform in 30 s and it crosses a signal on the station in 12 sec. Find the speed of the train in km/hr and the length of the train

Answer 1

Time difference while crossing platform and a signal is 30 - 12 = 18s.

=> Train travels 300m in 18s

=> Speed of train = 300/18 x 18/5 = 60 km/hr.

=> Length of train = 300/18 x 12 = 200m.

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Answer 2

Speed Time Problem

Let the length of  a train be x meter.

Let the speed of the train be y meter per sec.

Length of the platform is 300m.

Time taken to cross the signal is 12 seconds.

Time taken to cross the platform is 30 seconds.

$Time \ taken \ to \ cross \ the\ signal =\frac{length\ of \ train}{speed\ of\ train}\\\\\implies time\ taken(t)=12=\frac{x}{y}\\\\\implies12y=x$

and,

Time taken by train to cross the platform =$\frac{(length\ of \ train+length\ of \ platform)}{speed\ of \ train}$

$\implies 30=\frac{(x+300)}{y}\\\\\implies 30y=x+300$

putting the value of x in this equation,

$30y=12y+300\\\\\implies 18y=300\\\\\implies y=\frac{50}{3}m/s$

As question demands for speed in km/hr, so,

$\frac{50}{3}m/s=\frac{50}{3}\times\frac{18}{5}=60\ km/hr$

Hence speed of train is 60 km/hr.

The length of train is

$x=30y-300\\\\\implies x=30\times \frac{50}{3} -300=200m$

Hence, length of train is 200m.