Question

A passenger while boarding the plane slippe from the stairs and got hurt. the pilot took the passengers in the emergency clinic at the airport for the treatment due to this, plane got delayed half an hour. To reach the destination 1500km away in time, so that the passengers could catch the connection flight, the speed of the plane was increased by 250km/hr than the usual speed. What is the usual speed of the plane.

Answer 1

Let the original speed of the plane be x km/hr
Now speed $=(x+250)km/hr$
$t_1$ (travelled at original speed) $=\frac{1500}{x}$
$t_2$ (travelled at increased speed) $=\frac{1500}{x+250}$
According to question, $t_1-t_2=\frac{1}{2}hr$
$\frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}\frac{1500(x+250-x)}{x(x+250)}=\frac{1}{2}1500\times 250\times 2=x^2+250x{x}^2+250x-750000=0x^2+1000x-750x-750000=0x(x+1000)-750(x+1000)(x-750)(x+1000)=x$
$x=750,x=-1000$ (speed can't be negative)
So, speed of plane = 750~km/hr