Question

A train travelling at 54 km/h crosses a bridge
in 80 seconds. What is the length of the train, if
the length of the bridge is 800 m?​

Answer 1

Answer:-

$\red{\bigstar}$ Length of the train

$\large\leadsto\boxed{\sf{<strong>400 m</strong>}}$

• Given:-

Speed of the train = 54 km/hr

→ $\sf{54 \times \dfrac{5}{18} m/s}$

→ 3 × 5 m/s

→ 15 m/s

Time taken to cross the bridge = 80 sec.

Length of the bridge = 800 m

• To Find:-

Length of the train = ?

• Solution :-

Let the length of the train be 'x' m

Distance covered by train to cross the bridge (d) = Length of the train + Length of the bridge

→ d = (x + 800)m

We know,

$\boxed{ \sf Speed =\dfrac{Distance}{Time}}$

→ $\sf{15 = \dfrac{x + 800}{80}}$

→ $\sf{15 \times 80=x + 800}$

→ $\sf{1200 = x + 800}$

→ $\sf{1200 - 800 = x}$

→ $\sf{400 = x}$

→ $\boxed{\sf{x = 400}}$

Therefore, the length of the train is 400 m

Answer 2

$\large\bold{\underline{\underline{{Given:-}}}}$

▪️Speed of the train = 54 km/hr.

➛ $\sf\large\red{54 \times \frac{5}{8} }$

➛ $\sf\large\red{3 \times 1}$

➛ $\sf\large\red{15 \: m/s }$

▪️Time taken = 80 seconds.

▪️Length of the bridge = 800 m.

$\large\bold{\underline{\underline{{To\:Find:-}}}}$

▪️Length of the train.

$\large\bold{\underline{\underline{{Solution:-}}}}$

▪️Let length of the train be x.

${\boxed{{\bf{Distance \: travelled \: = speed \times time}}}}$

$\sf\large\green{= 15 \times 80}$

$\sf\large\green{= 1200 \: m}$

${\boxed{{\bf{Total \: distance \: travelled = length \: of \: bridge + length \: of \: train \: }}}}$

➛ $\sf\large\red{1200 = 800 + x}$

➛ $\sf\large\red{x = 1200 - 800}$

➛ $\sf\large\red{x = 400 \: m}$