Question

a train travelling at 144 km/hr crosses another train , having 50 mitter less length and traveling in opposite direction at 108 km/hr in 8 seconds. if smaller train cross a railway platform in 21 second then find longer train will cross same platform in how many seconds?

Answer 1

Answer:

this is an example of this question

Answer 2

Given :

Speed of first train = 144 km/hr

Speed of second train = 108 km/hr

Time taken = 8 seconds

if smaller train cross a railway platform in 21 second

To find : time taken by longer train cross the platform = ?

Solution :

Since they are travelling in opposite direction.

relative speed = $144+108=252\ km/hr=252\times \dfrac{5}{18}=70\ m/sec$

Let the length of first train be 'x'

Let the length of second train be 'x-50'

According to question, we get :

$\dfrac{x+x-50}{8}=70\\\\2x-50=8\times 70\\\\2x=560+50\\\\2x=610\\\\x=\dfrac{610}{2}\\\\x=305$

Length of smaller train = 305-50=255\ m

Let the length of platform be 'y'.

time taken to cross the platform = 21 second

Speed of smaller train = $108\times \dfrac{5}{18}=30\ m/sec$

Speed of longer train = $144\times \dfrac{5}{18}=40\ m/sec$

So, it becomes :

$\dfrac{255+y}{21}=40\\\\255+y=30\times 21\\\\255+y=630\\\\y=375$

So,longer train will take time:

$\dfrac{305+375}{40}=t\\\\\dfrac{680}{40}=t\\\\t=17\ sec$

Hence, longer train will take 17 seconds to cross the platform.