Question

A train traveling at a speed of 72 km/hr passes an electric pole in 30 seconds. Find the time taken by it to cross a bridge of length 900 m (in seconds)​

Answer 1

Given data : A train traveling at a speed of 72 km/hr passes an electric pole in 30 seconds.

To find : The time taken by it to cross a bridge of length 900 m (in seconds).

Solution :

Here, according to given,

→ speed of train = 72 km/hr

→ time taken by train to pass pole = 30 sec

→ length of bridge = 900 m

we need to convert dpeed of train into m/s

→ speed of train = 72 km/hr

→ speed of train = {72 * 1000}/{1 * 60 * 60}

→ speed of train = 72000/3600

→ speed of train = 20 m/s

Now, to find length of train, we take distance as length of train.

By formula of speed

→ speed = distance/time

→ 20 = distance/30

→ distance = 20 * 30

→ distance = 600 metre

Hence, length of train is 60 metre

when train crossed brigde it cover distance

= length of train + length of bridge

when train crossed brigde it cover distance

= 900 + 600

when train crossed brigde, it cover distance

= 1500 metre

Now, by formula of speed

→ speed = distance/time

→ 20 = 1500/time

→ time = 1500/20

→ time = 75 sec

Answer : Hence, time taken by train to cross bridge is 75 sec.

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Answer 2

Let length of train = L

Speed of train

$=72\:km/hr=\frac{72\times1000}{3600} \:m/s\\=\frac{720}{36} \:m/s\\=20\:m/s$

time taken to cross pole = 30 s

From figure 1,

distance travelled on crossing pole = AB = 20 m/s × 30 s = 600 m

⇒ AP + PB = 600 m

⇒ AP + AP = 600 m

⇒ 2L = 600 m

⇒ L = 300 m

In figure 2,

distance travelled by train to cross bridge (PQ) = distance travelled by head of train to go from P to D

= PD

= PQ + PD

= Length of bridge + Length of train (L)

= 900 m + 600 m

= 1500 m

Now, time taken by train to cross bridge (PQ) = time taken by head of train to go from P to D

$=\frac{PD}{speed\:of\:train} \\\\=\frac{1500\:m}{20\:m/s}\\=75\: s$

Therefore, time taken by train to cross bridge (PQ) is 75 seconds