Question

11. Find the length of the bridge in which a
train 140 m long travelling at 54 kmph
can cross in 30 seconds.
210 m​

Answer 1

Given,

Length of the train = 140 metres

Speed of the train = 55 km/h

Crossing time = 30 seconds

To find,

The length of the bridge.

Solution,

Let, the length of the bridge = x metres

[Assume, x as a variable to do the further mathematical calculations.]

To cross the bridge the train has to travel = Length of train + Length of bridge = (140+x) metres ... (1)

Now,

The train goes in,

1 hour = 54 km

3600 seconds = 54000 m

1 second = 54000/3600

30 seconds = 54000×30/3600 = 450 m ...(2)

By, comparing (1) and (2), we get that,

140+x = 450

x = 450-140

x = 310

Hence,the length of the bridge is 310 metres.

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

1.

For a moving body traveling a distance then

$\displaystyle \sf{ \:Time \: taken = \frac{Distance \: \: Covered}{Speed \: of \: the \: body} \: }$

2.

When a train is crossing a bridge then the in order to crossing the bridge the train has to travel distance = The length of the bridge + Length of the train

GIVEN

• A train is 140 m long
• The speed of the train is 54 kmph
• Time taken to cross the bridge is 30 seconds

TO DETERMINE

The length of the bridge

CALCULATION

Here The speed of the train is

$= \sf{ \: 54 \: \: kmph \: }$

$= \displaystyle \sf{ \: \frac{54 \times 1000}{3600} \: } \: \: metre \: / \: sec$

$= \displaystyle \sf{15} \: \: metre \: / \: sec$

Let x metre be the length of the bridge

Now in order to crossing the bridge the train has to travel distance = The length of the bridge + Length of the train

So the total distance covered by the train

= ( x + 140 ) metre

$\displaystyle \sf{ \:Time \: taken \: }$

$\displaystyle \sf{ \ = \frac{Distance \: \: Covered}{Speed \: of \: the \: body} \: }$

$= \displaystyle \sf{ \ \frac{x + 140}{15} \: } \: \: seconds$

According to the given condition

$\displaystyle \sf{ \ \frac{x + 140}{15} \: } \: \: = 30$

$\implies \sf{ \:x + 140 = 450 \: }$

$\implies \sf{ \: x = 310 \: }$

RESULT

THE LENGTH OF THE BRIDGE = 310 metre

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LEARN MORE FROM BRAINLY

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