Question

A journey of 192 km from a town A to town B takes 2 hours more by ordinary passenger train than a super fast train . If the speed of super fast train is 16 km/h more.
Find the speed of super fast train and passenger train.

Answer 1

Given the separation is $192km$ and let the speeds of ordinary,super fast trains be $v_o,v_s$ and time taken by them are $t_o,t_s$ respectively.From given data of speeds and times are;

$v_s=v_o+16$

$t_o=t_s+2$

we know the speed,time,distance relation

$time=\frac{distance}{speed}$

$\frac{192}{v_o}=\frac{192}{v_s}+2$

$192\times \frac{v_s-v_o}{v_o\times v_s}=2$

$v_0\times v_s=\frac{192\times 16}{2}$

$v_o(v_o+16)=1536$

$(v_o+8{)}^2=1536+64=1600={40}^2$

$v_o+8=40$

$v_o=32kmph,v_s=48kmph$

therefore speeds of ordinary,super fast trains are $32kmph,48kmph$.