Question

A train 100 meters long passes a bridge at the rate of 72 kilometers per hour in 25 seconds. What is the length of the bridge?

Answer 1

Answer:

$\boxed{\mathfrak{Length \ of \ the \ bridge \ (L_B) = 400 \ m}}$

Explanation:

$\rm Speed \: of \: train \: ( u_T ) = 72 \: km /hr \\ \\ \rm = 72 \times \frac{5}{18} \: m/s \\ \\ \rm = 20 \: m/s$

$\rm Length \: of \: train \: (L_T) = 100 \: m$

Let length of bridge be '$\rm L_B$'

For train to cross the bridge total distance to be covered by train (d) = $\rm L_T + L_B$

Time taken to cross (t) = 25 s

As we know,

$\bf Speed = \dfrac{Distance}{Time}$

So,

$\rm \implies u_T = \dfrac{d}{t} \\ \\ \rm \implies u_T = \dfrac{L_T + L_B}{t}$

By substituting values we get:

$\rm \implies 20 = \dfrac{100 + L_B}{25} \\ \\ \rm \implies 100 + L_B = 20 \times 25 \\ \\ \rm \implies 100 + L_B = 500 \\ \\ \rm \implies L_B = 500 - 100 \\ \\ \rm \implies L_B = 400 \: m$

Answer 2

★ QUESTION :

A train 100 metres long passes a bridge at the rate of 72 kilometres per hour in 25 seconds. What is the length of the bridge ?

GIVEN :

• A train 100 metres long passes a bridge
• Passing at the rate = 72 km (in 25 seconds)

[ Therefore, Speed of train during = 72km/hr]

TO FIND :

• The length of the bridge = ?

STEP - BY - STEP EXPLAINATION :

⟼ Passing at the rate (Speed) = 72km/hr

Therefore, we will have to change it into m/s form, so let us do it :

$⟹ \: 72 \times \frac{5}{18} \: ᴍ/s$

[ When reduced ]

⟹ 4 × 5 ᴍ/s = 20ᴍ/s

So, now we will have to consider length as 100 m

⟼ Considering here length of the train (AB) as 100 meters.

━━━━━━━━━━━━━━━━━━━━━━━━━

Assuming here length of the bridge as 'BC'

Therefore, all the distance covered ( Total distance covered) = AB + BC

Applying the formula, so that we will be able to find the length of the bridge :

♦ FORMULA USED :

• Speed = Distance / Time

[ Substituting the values as per the provided formula that is to be used for finding the appropriate length of the bridge ] :

➠ Speed = AB + BC / time

[ Applying the appropriate value ]

➠ 20 = 100 + BC / 25

➠ 100 + BC = 20 × 25

➠ 100 + BC = 500

[ Therefore, here we will shift the like and unlike value one side ] :

➠ BC = 500 - 100 [ Sign replaced ]

➠ BC = 400m

Hence, the length of the bridge = 400m