Question

An aircraft was to take off from a certain airport at 8 am but it was delayed by 30 min To make up for the lost time it was to increase its speed by 250 km/hr from the normal speed to reach its destination 1500 km on time What was the normal speed of the aircraft?

• A. 650 km/hr
• B. 750 km/hr
• C. 850 km/hr
• D. 1000 km/hr

Answer 1

Answer: (B)

750 km/hr

Let the normal speed of the aircraft be x km/hr $\therefore \frac{1500}{x}-\frac{1500}{250+x}=\frac{1}{2}\Rightarrow \frac{1500(250+x)-1500x}{x(x+250)}=\frac{1}{2}$
$\Rightarrow x^2+25x=2\times 1500\times 250\Rightarrow x^2+250x-750000=0$
$\Rightarrow x^2+1000x-750x-750000=0\Rightarrow x(x+1000)-750(x+1000)=0$
$\Rightarrow (x+1000)(x-750)=0\Rightarrow x=-1000or750$
Neglecting -ve values, x = 750 km/hr