Question

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

• A. 650 km/hr
• B. 950 km/hr
• C. 850 km/hr
• D. 750 km/hr

Answer 1

The correct option is D

750 km/hr

Let the usual speed of the plane be $x$ km/hr.

Then, time taken to cover 1500 km with the usual speed

$=\frac{1500}{x}hrs$

Time taken to cover 1500 m with the speed of $(x+250)km/hr=\frac{1500}{x+250}$

$\therefore \frac{1500}{x}=\frac{1500}{x+250}+\frac{1}{2}$

$\Rightarrow \frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}$

$\Rightarrow \frac{1500x+1500\times 250-1500x}{x(x+250)}=\frac{1}{2}$

$\Rightarrow \frac{1500\times 250}{x^2+250x}=\frac{1}{2}$

$\Rightarrow 750000=x^2+250x$

$\Rightarrow x^2+250x-750000=0$

$\Rightarrow x^2+1000x-750x-750000=0$

$\Rightarrow x(x+1000)-750(x+1000)=0$

$\Rightarrow (x+1000)(x-750)=0$

$\Rightarrow x=-1000or,x=750$

$\Rightarrow x=750$
[$\because$ speed cannot be negative]

Hence, the usual speed of the plane is 750 km/hr