Question

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

• A. 1000 km/hr
• B. 750 km/hr
• C. 800 km/hr
• D. 680 km/hr

Answer 1

The correct option is B 750 km/hr

Let the usual speed of plane be $xkm/hr$

and the increased speed of the plane be $ykm/hr.$

$\Rightarrow$ $y=(x+250)km/hr$

Distance $=1500km$ [Given]

According to the question,

(Scheduled time) - (time taken at increased speed) = 30 minutes = 0.5 hours.

$\frac{1500}{x}-\frac{1500}{y}=\frac{1}{2}$

$\frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}[\because Time=\frac{Distance}{Speed}]$

$\Rightarrow \frac{1500x+375000-1500x}{x(x+250)}=\frac{1}{2}$

$\Rightarrow$ $x(x+250)=750000$

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

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

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

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

$\Rightarrow$ $x=750orx=-1000$

But speed cannot be negative.

$\therefore$ The usual speed is 750 km/hr.