Question

Solve the following
A train travels at a retain average speed for a distance of $63km$ and then travels a distance of $75km$ at an average speed of $6km/h$ more than its original speed. If it takes $3hr$ to complete total journey find its original average.

Answer 1

let the initial speed be $x$

therefore time taken to cover first $63$ km is $=\frac{63}{x}$

now as speed is increased by $6$ time taken to cover next $75$ km is $\frac{75}{(x+6)}$

given $\frac{63}{x}+\frac{75}{(x+6)}=3$[as total time is 3 hours]

$\Rightarrow 63(x+6)+75x=3x(x+6)$

$138x+378=3x^2+18x\Rightarrow 3x^2-120x-378=0$

therefore $x=\frac{-(-120)\pm \sqrt{{(-120)}^2-\mathrm{4.3.}(-378)}}{2.3}\Rightarrow x=\frac{120\pm 137.608}{6}=42.9346$