A plane left 30 mins later than the scheduled time and in order to rea

1.	A plane left 30 mins later than the scheduled time and in order to reach is destination 1500 I'm away in time it has to increase is speed by 250 km/hr from is usual speed . Find it's usual speed.
Answer» GIVEN : A PLANE left 30 mins later than the scheduled time. It increase SPEED by 250 km/hr. TO FIND : Usual speed = ? SOLUTION : To find the usual speed = ? We know that, Let x be the usual speed of the plane. Increased speed is = x + 250. The time taken by plane in usual CIRCUMSTANCES, $\sf t_1 \ = \ \dfrac {distance}{speed}$ $\implies \sf t_1 \ = \ \dfrac {1500}{x}$ Time taken by plane due to delay, $\implies \sf \dfrac {distance}{x + 250}$ Difference in times = Delay in departure. $\implies \sf \dfrac {1500}{x} \ - \ \dfrac {1500}{x+250}$ $\implies \sf \dfrac {x + 250 - x}{x^{2} + 250x}$ $\implies \sf x^{2} \ + \ 250x \ - \ 750000 \ = \ 0$ $\implies \sf x^{2} \ + \ 1000x \ - \ 750x \ - \ 75000 \ = \ 0$ $\implies \sf x(x + 1000) \ - \ <klux>750</klux>(x + 1000) \ = \ 0$ $\implies \sf (x - 750) (x + 1000) \ = \ 0$ $\qquad \qquad \large \blue {\boxed {\tt x \ = \ 750}}$ $\therefore$ The usual speed of the plane is 750 km/hr.