Question

A trains travels at a certain speed for a distance of $63km$ & then travels a distance $72km$ at an average speed of $6km/h$ more than its original speed. If it takes $3h$ to complete the total journey then find its original avg speed

Answer 1

Given distance = 63 km.

Original speed of trian = x cm/hr.

time $=\frac{distance}{speed}=\frac{63}{x}$ hrs

And it travels a distance of 72 km at a avg speed of 6 km / hr more than original speed.

distance = 72 km

speed = (x+6) km / m.

time $=\frac{72}{2+6}$ hrs.

If it takes 3 hrs to complete the whose journey $\frac{63}{x}+\frac{72}{x+6}$ = 3 hrs

63(x+6)+72x = 3x(x+6)

21(x+6)+24x = x(x+6).

$45x+21\times 6=x^2+6x$

$x^2-39x-126=0$

(x-42) (x+3) = 0

$\therefore$ x = 42 [original avg speed]