Question

The length of the bridge, which a train $130\mathrm{meters}$ long and traveling at $45\mathrm{km}/\mathrm{hr}$ can cross in $30$ seconds, is:

• A. $200\mathrm{m}$
• B. $225\mathrm{m}$
• C. $245\mathrm{m}$
• D. $250\mathrm{m}$

Answer 1

The correct option is C

$245\mathrm{m}$

The explanation for the correct option.

First, convert the speed of the train into $\mathrm{m}/\mathrm{s}$.

$$\begin{gathered} \because 1\mathrm{km}/\mathrm{h}=\frac{5}{18}\mathrm{m}/\mathrm{s} \\ \therefore 45\mathrm{km}/\mathrm{h}=45\times \frac{5}{18} \\ \Rightarrow =12.5\mathrm{m}/\mathrm{s} \end{gathered}$$

Let us consider the length of the bridge is $l$.

$$\begin{gathered} \because \frac{\mathrm{Distance}}{\mathrm{speed}}=\mathrm{time} \\ \therefore \frac{130+l}{30}=12.5 \\ \Rightarrow 130+l=12.5\times 30 \\ \Rightarrow 130+l=375 \\ \Rightarrow l=375-130 \\ \Rightarrow l=245\mathrm{m} \end{gathered}$$

Hence, the option C is correct.