Question

a train covers a distance of 780 km/hr . had the speed been x-5 km/hr, the time taken to cover the same distance would have increased by 1 hour.​

Answer 1

Answer:

Given :

• Distance = 780 km
• if speed reduced by 5 km/hr.It would take 1 hour more .

Solution:

   Let 'x' be the speed of train. ($\boxed{Time=\dfrac{Distance}{Speed}}$ )

Hence,time taken by the train becomes

$\dfrac{780}{x}$

        Now,it is given that  if speed reduced by 5 km/hr.

$\therefore \dfrac{780}{x-5}$

then,It would take 1 hour more

$\implies \dfrac{780}{x-5}=\dfrac{780}{x}+1$

Now, we can cross multiply and go forward

$\dfrac{780}{x-5}=\dfrac{780}{x}+1\\\\\implies \dfrac{780}{x-5}=\dfrac{780+x}{x}\\\\or,x(780)=(x-5)(780+x)\\or,780x=780x+x^2-3900-5x\\\\or,after\:re-arranging\\x^2-5x-3900=0\\\\\using\:quadratic\:equation.\\\\\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\ \dfrac{-(-5)\pm \sqrt{5^2-4(-3900)(1)}}{2(1)}\\\\\implies \dfrac{5\pm\sqrt{15625}}{2}\\\\ \implies \dfrac{5\pm 125}{2}\\\\or, x =65km/hr or -60km/hr \\since\:speed\:cannot\:be\:negative\\\\ \textbf{speed=65km/hr}$