Question

A train running at a uniform speed passes a bridge $275$ m long in $15$ seconds and another bridge $425$ m long in $21$ seconds. Find the speed of the train in km/hr.

• A. $28$ km/hr
• B. $110$ km/hr
• C. $60$ km/hr
• D. $90$ km/hr

Answer 1

The correct option is D $90$ km/hr

Solution:
Let the speed of the train be 's' m\sec
and length of train be 'L' m.
Given Equation: Bridge of distance 275 m and time is 15 seconds.
Bridge of distance 425 m and time is 21 seconds.
Factor to consider is length of Train.
Hence total length $=Bridgelength+Lengthoftrain$
According to the formula:
Speed $=\frac{Distance}{Time}$
Equation 1 . s $=\frac{L+275}{15}$
Similarly for equation 2. s$=\frac{L+425}{21}$
From Equation 1 and Equation 2.
$\frac{L+275}{15}=\frac{L+425}{21}$
$21\times \left(L+275\right)=15\times \left(L+425\right)$
$21\times L+21\times 275=15\times L+15\times 425$
$6\times L=600$
$L=100$ m.
To calculate speed of train Substitute value of L in equation 1 or equation 2.
Equation 1.
$s=\frac{L+275}{15}$
$s=\frac{100+275}{15}$

= $25$ m\s
To calculate speed in km\hr.
$1$km = $1000$ m
$1$ hr = $3600$ sec
$1$ m\sec = $\frac{3600}{1000}$
= $\frac{18}{5}$
$25$ m\sec =$25\times \left(\frac{18}{5}\right)$ km\hr
= $90$ km\hr