Question

A train running at uniform speed passes a bridge 300 m long in 15 sec and another bridge 450 m long in 21 sec. Find:- (i) The length of the train (ii)The speed of the train in km/h

Answer 1

Length of the train = L meters.
Distance travelled by the train to cross the bridge is the length of the bridge plus length of the train.

Speed of the train = distance / time interval
           = (300 + L) m / 15 sec  =  (450 + L) / 21 sec
   =>    21 (300 + L)  = 15 (450 + L)
   =>    2100 + 7 L = 2250 + 5 L
   =>    2 L = 150
   =>  L = 75 meters.

Speed of the train = (300 + 75) meters / 15 sec = 25 m/sec
                 = 25 * 18/5 = 90 km/hour

Answer 2

$\huge\underline\mathfrak\red{Answer}$

Let the length of train be = L

So, Distance travelled by train to cross the bridge is the,Length of the bridge+trains length

Speed of train = Distance travelled

=(300+L) m/(450+L) = 15/21

=(300+L)/(450+L) = 3/7

=[Cross multiple of 3/7]

=7(300+L) = 5(450+L)

=2100+7L = 2250+5L

=2250-2100 = 7L-5L

=150=2L

=150/2=L

=75=L

Speed of the train = (300+75)/15seconds

(25m/second)